Answer:
5 weeks
Step-by-step explanation:
the two linear equations are:
sibling (A) and sibling (B)
y = 10x + 25 and y = 5x + 50
where y = mx + c
and x represents the number of weeks
after how many weeks will their savings accounts have the same amount of money i.e. for which value of x will both equations have the same value
inserting the value of x in both equations:
for x = 2.5 A = 50 and B = 62.5
for x = 5 A = 75 and B = 75
for x = 15 A = 175 and B = 125
for x = 75 A = 775 and B = 425
thus, after 5 weeks both siblings A and B will have the same amount of money in their accounts
In a math class with 28 students, a test was given the same day that an assignment was due. There were 18 students who passed the test and 19 students who completed the assignment. There were 15 students who passed the test and also completed the assignment. What is the probability that a student passed the test given that they completed the homework
Answer:
0.789 to 1 or 78.9 percent chance
Step-by-step explanation:
15 did the homework and passed
19 did the homework
therefore, only 4 people who completed the homework and failed the test.
so, 15/19= 0.789, or 78.9 percent. or a 0.789 to one chance
Huh, where HI~=IJ, m angle H = (3x+10), and m angle I = (6x - 20), find the measures of angles H, I, and J
Answer:
m∠J is approximately equal to m∠H and m∠I, so it is also approximately 40 degrees.
Step-by-step explanation:
To find the measures of angles H, I, and J, we can use the fact that HI is approximately equal to IJ. Let's denote the measures of angles H, I, and J as m∠H, m∠I, and m∠J, respectively.
Given that HI is approximately equal to IJ, we can say that m∠H is approximately equal to m∠J.
So, m∠H ≈ m∠J.
We're also given that m∠H = 3x + 10 and m∠I = 6x - 20.
Since m∠H ≈ m∠J, we can equate their expressions:
3x + 10 ≈ 6x - 20.
To solve for x, we can subtract 3x from both sides and add 20 to both sides:
10 + 20 ≈ 6x - 3x.
30 ≈ 3x.
Dividing both sides by 3, we find:
10 ≈ x.
Now that we have the value of x, we can substitute it back into the expressions for m∠H and m∠I:
m∠H = 3x + 10 = 3(10) + 10 = 30 + 10 = 40.
m∠I = 6x - 20 = 6(10) - 20 = 60 - 20 = 40.
Therefore, the measures of angles H, I, and J are:
m∠H = 40 degrees,
m∠I = 40 degrees,
m∠J is approximately equal to m∠H and m∠I, so it is also approximately 40 degrees.
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x+2y=3,3x+4y=1 find X and y
To find the values of x and y in the system of equations:
Equation 1: [tex]x + 2y = 3[/tex]
Equation 2: [tex]3x + 4y = 1[/tex]
We can solve the system using the method of substitution or elimination. Here, I will demonstrate the method of substitution:
Step 1: Solve Equation 1 for x:
[tex]x = 3 - 2y[/tex]
Step 2: Substitute the value of x from Step 1 into Equation 2:
[tex]3(3 - 2y) + 4y = 1[/tex]
Step 3: Simplify and solve for y:
[tex]9 - 6y + 4y = 1[/tex]
[tex]-2y = 1 - 9[/tex]
[tex]-2y = -8[/tex]
[tex]y = \frac{-8}{-2}[/tex]
[tex]y = 4[/tex]
Step 4: Substitute the value of y back into Equation 1 to find x:
[tex]x + 2(4) = 3[/tex]
[tex]x + 8 = 3[/tex]
[tex]x = 3 - 8[/tex]
[tex]x = -5[/tex]
Therefore, the solution to the system of equations is:
[tex]x = -5[/tex]
[tex]y = 4[/tex]
[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]
♥️ [tex]\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]
Answer: X=-2 & Y=5/2
Step-by-step explanation:
STEP 1: Find the given equations
x+2y=3 and 3x+4y=1
STEP 2: Try to equate any of the terms by multiplying either of the equations.
HERE, we can multiply the equation x+2y=3 by 2
WE GET, 2x+4y=6 and we can see that 4y terms is common in both te equations
STEP 3: cancel out the matching terms by simple addition or subtraction of the equations.
after solving we get, x=-2.
STEP 4: put the value of x in any of the two quations to get the value of y.
WE GET, the value of y as 5/2.
check the attached image for a better understanding.
LOTS OF POINTS Can someone provide the correct answer, and tell me what I did wrong here?
The height of the given triangle will be 13.416 cm.
Given a right-angle triangle that has a hypotenuse of 14 cm, height of x, and base of 4 cm.
The Pythagorean theorem is a fundamental principle in geometry that establishes a relationship between the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Applying the Pythagorean theorem, we can write:
[tex]14^2 = 4^2 + x^2[/tex]
Simplifying the equation:
[tex]196 = 16 + x^2[/tex]
Subtracting 16 from both sides:
[tex]180 = x^2[/tex]
Taking the square root of both sides:
x = √180 = 6√5
Simplifying the square root:
x ≈ 13.416 cm
Therefore, the height (x) of the right-angle triangle is approximately 13.416 cm.
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Help me with this please!
The solution is: Option D has the correct data points and so is the right answer.
We have,
A function is a mathematical way of representing relation between two variables.
The function given is
y = 2x²
For x = - 2, y = -2(- 2)² = -8
For x = - 1, y = -2(- 1)² = -2
For x = 0, y = -2(0)² = 0
For x = 1, y = -2(1)² = -2
For x = 2, y = -2(2)² = -8
the table of x-y will be:
x - 2 - 1 0 1 2
y -8 -2 0 -2 -8
The graph is attached with the answer.
The parabola opens downward and has the data points as mentioned above .
The Graph B best represents a parabola ,
Therefore Option D is the correct answer.
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complete question:
Complete the following table using the equation: Y = negative 2 x Squared x -2 -1 0 1 2 y Plot the points on a graph and determine which graph best represents the equation. Graph A On a coordinate plane, a parabola opens up. It goes through (negative 1, 2), has a vertex at (0, 0), and goes through (1, 2). Graph B On a coordinate plane, a parabola opens down. It goes through (negative 1, negative 1), has a vertex at (0, 0), and goes through (1, negative 1). a. 8, 2, 0, 2, 8; Graph A b. -8, -2, 0, -2, -8; Graph A c. 8, 2, 0, 2, 8; Graph B d. -8, -2, 0, -2, -8; Graph B Please select the best answer from the choices provided A B C D
During one year, the population of a town increased by 2% but during the next year it diminished by 2%. If at the end of the second year the population was 6,25,000, what was the population at the beginning?
Answer:
614,818.71
Step-by-step explanation:
hope it helps
Answer:
6,25,250
Step-by-step explanation:
let initaial population be "x"
after increasing by 2%
x'=x+x*2%
x'=102x/100
x' is decreased by 2% and population reached 625000,so,
625000=102x/100-2%*102x/100
625000=102x/100-51x/2500
625000=2499x/2500
2499x=625000*2500
x=1562500000/2499
x=625250.1
complete population is only counted so,
x=625250
initial population =625250
Need answers too this I will give you a award
Answer:
2 . figures have a volume that is greater than 600 in3.
Step-by-step explanation:
2.2. If using the following formula to compute an approximation of f’(z):
F(a) & az Fle + 2h) + 8F(e + h) — 8f(w— h) + fw — 2A],
2.2.1 find the order of convergence as h — 0.
The order of convergence of the formula as h approaches 0 is at least 1.
To determine the order of convergence as h approaches 0 for the approximation of f'(z) using the given formula, we need to analyze the behavior of the formula as h becomes smaller.
Let's rewrite the formula in a more structured form for better clarity:
f'(z) ≈ [F(z + 2h) - 8F(z + h) + 8F(z - h) - F(z - 2h)] / (12h)
As h approaches 0, we can rewrite the formula using the limit notation:
f'(z) ≈ lim(h→0) [F(z + 2h) - 8F(z + h) + 8F(z - h) - F(z - 2h)] / (12h)
In this case, we can simplify the limit expression by dividing both the numerator and denominator by h:
f'(z) ≈ lim(h→0) [F(z + 2h)/h - 8F(z + h)/h + 8F(z - h)/h - F(z - 2h)/h] / 12
f'(z) ≈ lim(h→0) [F'(z) - 8F'(z) + 8F'(z) - F'(z)] / 12
f'(z) ≈ lim(h→0) 0 / 12
f'(z) ≈ 0
From this analysis, we see that as h approaches 0, the f'(z) approaches 0. This means that the order of convergence of the given formula is at least 1.
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which word means a location in space?
a. line
b. plane
c. point
d. ray
Answer:
C.
Step-by-step explanation:
I think the answer is C. or a point because a point is like a location in space and the question is asking which word means a location in space.
3.
Find out the values of x and y from the following ordered pairs.
b.
(x+2, y - 1) = (2, 3)
(x, y)=(5,6)
(3x, 8) = (12, y - 1)
(2x+1, y - 2) = (1, 2)
(x+1, 8) =(3, 2y)
(x-2, y + 1) =(4, 2y)
(2x + y, 3) = (5, 3y)
(x+y, x-3) = (8,4)
(2x + 3y, 2x) = (20, x +4)
Answer:
see below
Step-by-step explanation:
b.
(x+2, y - 1) = (2, 3)
We have two equations:
x + 2 = 2
y - 1 = 3
Solving for x, we get:
x = 0
Solving for y, we get:
y = 4
Therefore, the values of x and y are 0 and 4, respectively.
Use the image to answer the question pls and Ty
100 Points! Algebra question, photo attached. Please show as much work as possible. Thank you!
A. The distributions of the periods is that using the five number summary is that
The 7th Period has higher minimum and lower maximumThe 3rd period is more spread (from the quartiles)The 7th Period has higher medianB. The box and whisker plot of the periods is attached
A. Comparing the distributions of the periodsFrom the question, we have the following parameters that can be used in our computation:
7th Period
66, 72, 77, 78, 78, 80, 82, 84, 84, 87, 88, 88, 89, 89, 90 92, 92, 93, 94, 94 96, 96
3rd Period
52, 60, 62, 64, 64, 65, 68, 71, 72, 74, 75, 76, 78, 79, 83, 84, 85, 88, 89, 93, 94, 97
The distributions of the periods will be compared using the five-number summaries
Using a graphing tool, the five-number summaries are:
7th Period
Minimum: 66Lower Quartile Q1: 79.5Median: 88Upper Quartile Q3: 92.25Maximum: 963rd Period
Minimum: 52Lower Quartile Q1: 64.75Median: 75.5Upper Quartile Q3: 85.75Maximum: 97B. Creating a box and whisker plot of the periodsThe box and whisker plot of the periods is added as an attachment
From the box and whisker plot attached, we can see the five-number summaries of the periods
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Mr. Khumalo has a Standard Bank Account. The cash deposiverser d counter (branch deposit) services includes air for of R10,39 plus K1,95 per R100 or part thereof, with a mininium charge of R16,00. What is the minimum amount that a person can be chaped for a cash deposit Mr Khumale deposited R4 550,00 over the counter at Standard Bank (2)
The minimum amount that Mr. Khumalo can be charged for the cash deposit is R99.12.
To calculate the minimum amount charged for a cash deposit over the counter at Standard Bank, we'll use the given information.
The deposit charge includes an initial fee of R10.39, and an additional fee of K1.95 per R100 or part thereof, with a minimum charge of R16.00.
First, we calculate the additional fee based on the deposit amount:
Additional fee = (Deposit amount / 100) x K1.95
For Mr. Khumalo's deposit of R4,550.00:
Additional fee = (4,550.00 / 100) x 1.95
Additional fee = 88.725
Next, we compare the additional fee to the minimum charge of R16.00:
If the additional fee is less than the minimum charge, the minimum charge applies. Otherwise, the additional fee is charged.
Since the additional fee of R88.725 is greater than the minimum charge of R16.00, the additional fee will be charged.
Finally, we add the initial fee and the additional fee to get the total charge:
Total charge = Initial fee + Additional fee
Total charge = R10.39 + R88.725
Total charge = R99.115
Therefore, the minimum amount that Mr. Khumalo can be charged for the cash deposit is R99.12.
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Clara graphed her reading fluency scores for 6 weeks. 99, 88, 97, 107, 100, 109 What is the median of the scores?
Answer:
99.5
Explanation:
First, you would put the numbers into order from least to greatest.
99, 88, 97, 107, 100, 109
Which would be:
88, 97, 99, 100, 107, 109
Median is the middle of the number line, so you would cross off a number from each side until you find the middle.
99, 100
You would end up with two numbers, which you will have to find the mean of. In order to do so, you need to add them together then divide by 2 because there are 2 numbers.
99 + 100 = 199
199/2 = 99.5
BK plays a game, which assigns a number (Z)that is the continuous random variable with the density function
(z) =1/5,0≤z≤5
0, otherwise.
If the game assigns a number less than or equal to, then he loses 10 dollars, on the other hand, if the game assigns a number larger than, then he will gain 10 dollars. (a) Find the expected profit of the game. (b) Find the variance of the profit. (c) If you were to play this game 10 times, what is the probability that you gain 20 dollars?
(a) The expected profit of the game is $0. (b) The variance of the profit is 0. (c) The probability of gaining $20 in 10 plays is 0.
Answers to the questionsTo solve the given problem, we'll calculate the expected profit, variance of the profit, and the probability of gaining $20 in 10 game plays.
(a) Expected Profit:
To calculate the expected profit, we need to multiply the potential profit or loss with its corresponding probability and sum them up.
Profit (X) = Gain - Loss = $10 - $10 = $0
Probability of gaining: P(X = $0) = P(Z > 5) = 0 (since Z is only defined up to 5)
Expected Profit (E(X)) = $0 * P(X = $0) = $0
(b) Variance of the Profit:
The variance can be calculated using the formula: Var(X) = E(X^2) - (E(X))^2.
In this case, since the profit is always zero, the variance will also be zero.
Variance of the Profit (Var(X)) = 0 - (0)^2 = 0
(c) Probability of Gaining $20 in 10 plays:
Since each play is independent, the probability of gaining $20 in a single play is 0. Since the probability of gaining is 0 for each play, the probability of gaining $20 in 10 plays will also be 0.
Probability of gaining $20 in 10 plays = 0
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An apple orchard's workers pick 14,446 apples in the month of October. A sample of 109 of these apples shows that 48 of them are damaged and bruised. What is the best estimate of the number of apples picked at the orchard in October that are bruised and damaged?
the ratio of the heights of two cylinders is 1:3. if the volume of the smaller cylinder is 67cm3, find the volume of the larger cylinder
PLEASE ANSWER ASAP
The volume of the larger cylinder is 201 cm³.
Given that,
Ratio of the heights of two cylinders = 1 : 3
We have to find the volume of the larger cylinder.
The formula to find the volume of a cylinder is,
Volume of cylinder = π r² h, where r is the radius and h is the height of the cylinder.
Let height of smaller cylinder = h
Height of larger cylinder = 3h
π r² (h) = 67
Volume of larger cylinder = π r² (3h)
= 3 [π r² (h)]
= 3 × 67
= 201 cm³
Hence he volume is 201 cm³.
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1. Write a polynomial of degree 3 with zeros
x = 3,x= -4, and x = 5.
The polynomial of degree 3 with zeros at x = 3, x = -4, and x = 5 is P(x) = x^3 - 4x^2 - 17x + 60.
To construct a polynomial of degree 3 with zeros at x = 3, x = -4, and x = 5, we can use the fact that the polynomial can be written as a product of linear factors corresponding to each zero.
The factor corresponding to x = 3 is (x - 3).
The factor corresponding to x = -4 is (x + 4).
The factor corresponding to x = 5 is (x - 5).
To obtain the polynomial, we multiply these factors together:
P(x) = (x - 3)(x + 4)(x - 5)
Expanding this expression gives us:
[tex]P(x) = (x^2 - 3x + 4x - 12)(x - 5)[/tex]
[tex]= (x^2 + x - 12)(x - 5)[/tex]
[tex]= x^3 - 5x^2 + x^2 - 5x - 12x + 60[/tex]
[tex]= x^3 - 4x^2 - 17x + 60[/tex].
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Finding Missing Angles in a Polygon
The missing angle is 25 degrees.
We are given that;
A polygon with 6 side have interior angles 90, 98, 140, x, 155, 112
Now,
we can write:
S = (6 - 2) × 180 degrees
S = 4 × 180 degrees
S = 720 degrees
We know that the sum of the given interior angles is:
90 + 98 + 140 + x + 155 + 112 = 695 + x
Since the sum of the interior angles of a polygon with 6 sides is equal to 720 degrees, we can write:
695 + x = 720
Solving for x, we get:
x = 25 degrees
Therefore, by the polygon the answer will be 25 degrees.
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Please help I’ll mark you as brainliest if correct!
The cosD is √53/9 from the given triangle which is adjacent side by hypotenuse
The triangle DEF is a right triangle
We know that cosine function is a ratio of adjacent side and hypotenuse
The adjacent side of angle D is DE
We have to find the length of DE by using Pythagoras theorem
DE²+EF² =DF²
DE²+28=9²
DE²=81-28
DE²=53
Take square root on both sides
DE=√53
So cosD=√53/9
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You deposit $300 in an account that earns simple interest at an annual rate of 6.5%.
If no other deposits or withdrawals were made, what is the total amount of money in the account at the end of 8 years?
Total amount of money in the account will be $456.
How much money will be in the account after 8 years?Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest.
The formula for simple interest is: Simple Interest = Principal × Rate × Time
Principal (P) is $300
Rate (R) is 6.5%
Time (T) is 8 years.
Simple Interest = $300 × 0.065 × 8
Simple Interest = $156
Total Amount = Principal + Simple Interest
Total Amount = $300 + $156
Total Amount = $456.
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A system of equations is created by using the line represented by 2 x + 4 y = 0 and the line represented by the data in the table below.
x
y
–1
8
3
–4
5
–10
6
–13
What is the x-value of the solution to the system?
A specific X-value for the solution ,-4 is not equal to -3/2.
The x-value of the solution to the system of equations, we need to solve the given equation and the line represented by the data in the table. Let's begin by examining the first equation, 2x + 4y = 0.
We can rewrite this equation in terms of y:
4y = -2x
y = (-2/4)x
y = (-1/2)x
Now, let's use the data from the table to create a system of equations:
For the first data point (-1, 8):
y = (-1/2)x
8 = (-1/2)(-1)
8 = 1/2
Since 8 is not equal to 1/2, the first data point does not satisfy the equation.
For the second data point (3, -4):
y = (-1/2)x
-4 = (-1/2)(3)
-4 = -3/2
Again, -4 is not equal to -3/2, so the second data point does not satisfy the equation.
We can continue this process for the remaining data points, but from the information given, it seems that none of the data points satisfy the equation. Therefore, there is no solution to the system of equations.
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If 10 teenagers can eat 72 slices of pizza, how many slices are needed to feed 20 teenagers?
what is the value of the underlined digit in the number 27,416,385. 4 is the underlined number.
The value of the underlined digit in the number 27,416,385.( 4 is the underlined number.) is the hundred thousandths place.
How can the digits be known?The symbols, from 0 to 9 can be described as a digit. For instance, the numbers 2 and 3 are used to represent the number 23. however amount is represented by a number.
It should be noted that It may be expressed using one, two, three, or even more digits however only single symbol used to represent a number is a digit in the case above we can see that 4 is the hundred thousandths place.
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You are purchasing a used car for $9,000. How much interest would you pay at 9.6% APR if you had the
loan for 5 years?
One would pay $5,232.96 in interest over the 5-year loan term.
How much interest would you pay at 9.6% APR?To get interest paid on the loan, we will the formula for compound interest [tex]Interest = Principal * (1 + Annual Interest Rate)^{Number of Years} - Principal[/tex]
The principal is the loan amount which is $9,000.
The annual interest rate is 9.6%
The number of years is 5.
Interest = $9,000 * (1 + 0.096)^(5) - $9,000
Interest = $9,000 * 1.58144018701 - $9,000
Interest = $5,232.96168
Interest = $5,232.96.
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A soccer player jumps up and heads the ball while it is 7 feet above the ground. If the function
y = -16t squared + 20t + 7 represents this situation, about how long will it take the ball to hit the ground?
Answer:
3.3 seconds
Step-by-step explanation:
To find the time it takes for the ball to hit the ground, we need to solve the equation y = 0, since the ball will be on the ground when its height (y) is zero.
The equation given is:
y = -16t^2 + 20t + 7
Setting y to zero:
0 = -16t^2 + 20t + 7
To solve this quadratic equation, we can either factor it or use the quadratic formula. In this case, factoring may not be straightforward, so let's use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = -16, b = 20, and c = 7. Substituting these values into the quadratic formula:
t = (-20 ± √(20^2 - 4(-16)(7))) / (2(-16))
t = (-20 ± √(400 + 448)) / (-32)
t = (-20 ± √848) / (-32)
Simplifying further:
t = (-20 ± √(16 * 53)) / (-32)
t = (-20 ± 4√53) / (-32)
Now we have two possible solutions for t:
t1 = (-20 + 4√53) / (-32)
t2 = (-20 - 4√53) / (-32)
Since time cannot be negative in this context, we can disregard the negative solution.
t ≈ (-20 + 4√53) / (-32)
Calculating this value:
t ≈ 3.3 seconds (rounded to one decimal place)
Therefore, it will take approximately 3.3 seconds for the ball to hit the ground.
Drake predicted that he would be able to make
16 more pancakes with the remainder of his
mix. However, he only made 10 pancakes.
What was Drake's percent error?
Hint: Percent error =
Prediction - Actual |
Actual
x 100
Round to the nearest percent.
[?]%
The box of pancake says that it makes 10 pancakes but sam is able to make 8 pancakes from the ingredient. Here the number 10 represents Theoretical yield.
Here,
Theoretical yield can be defined as the product received from the complete conversion of the limiting reactant in a chemical process.
It is the amount of product resulting from a theoretical chemical reaction and it is not the same as the amount you'll actually get from a reaction in the lab.
Theoretical yield is commonly expressed in terms of grams or moles. the actual yield is the amount of product actually produced by a reaction. Actual yield is usually a smaller quantity because few chemical reactions proceed with 100% efficiency because of loss recovering the product and because other reactions may be occurring that reduce the product. so 10 here is a theoretical yield bot the actual yield.
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complete question:
Decide whether the following scenarios represent theoretical or actual yields. sam follows the directions on a box of pancake mix. the box says that it makes 10 pancakes, but he is able to make 8 pancakes from the ingredients. in this case, the number 10 represents which type of yield?
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Write with fractional exponents. (Do not use parentheses.)
Answer:
4[tex]y^{\frac{3}{2} }[/tex]
Step-by-step explanation:
using the rule of exponents/ radicals
[tex]\sqrt[n]{a^{m} }[/tex] = [tex]a^{\frac{m}{n} }[/tex]
then
4 [tex]\sqrt{y^{3} }[/tex]
= 4[tex]y^{\frac{3}{2} }[/tex]
If sides BD and DC have the same length, what is the length of side BC?
Diagram shows triangle BAD shares its hypotenuse BD with vertical leg BD of right triangle BDC. In triangle BDC, right angle is marked at vertex D. In triangle BAD, right angle is marked at vertex A. Sides AB and AD are labeled 1 and 1.
A.
B.
C.
D.
E.
Answer:
C. 2 units
Step-by-step explanation:
In right triangle ABD, BD is the hypotenuse and AB and AD are the legs of the right triangle each with a length of 1 unit
By the Pythagorean Thereom
hypotenuse² = sum of squares of each of the other sides
BD² = AB² + AD² = 1² + 1² = 1 + 1 = 2
In right triangle BCD, BC is the hypotenuse and we are given BD = DC
BC² = BD² + DC² = BD² + BD² =2 BD² = 2 · 2 = 4
BC = √4 = 2 units
=) A shopkeeper, selling an object at a discount of 25% loses Rs. 125. If he allow 10% discount, he gains Rs. 250. Find the marked price and the cost price of the article.
The marked price of the article is approximately Rs. 833.33, and the cost price is Rs. 500.
Let's assume the marked price of the article is M and the cost price is C.
According to the given information:
When the shopkeeper sells the object at a discount of 25%, he incurs a loss of Rs. 125. This means that the selling price (S) is 25% less than the marked price (M) and it is equal to the cost price (C) minus Rs. 125.
S = C - Rs. 125
S = M - 0.25M
C - Rs. 125 = M - 0.25M
When the shopkeeper sells the object at a discount of 10%, he gains Rs. 250. This means that the selling price (S) is 10% less than the marked price (M) and it is equal to the cost price (C) plus Rs. 250.
S = C + Rs. 250
S = M - 0.10M
C + Rs. 250 = M - 0.10M
Now we can solve these two equations simultaneously to find the marked price (M) and the cost price (C) of the article.
C - Rs. 125 = M - 0.25M --> C = 0.75M - Rs. 125 (Equation 1)
C + Rs. 250 = M - 0.10M --> C = 0.90M - Rs. 250 (Equation 2)
Setting Equation 1 equal to Equation 2:
0.75M - Rs. 125 = 0.90M - Rs. 250
Rearranging the equation:
0.90M - 0.75M = Rs. 250 - Rs. 125
0.15M = Rs. 125
M = Rs. 125 / 0.15
M = Rs. 833.33 (approx.)
Substituting the value of M back into Equation 1 to find C:
C = 0.75M - Rs. 125
C = 0.75 * 833.33 - Rs. 125
C = Rs. 625 - Rs. 125
C = Rs. 500
Therefore, the marked price of the article is approximately Rs. 833.33, and the cost price is Rs. 500.
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