Two-thirds of a number is two more than one-half of another number. The sum of the number is 129. Find the numbers.​

Answers

Answer 1

Answer: 57 ; 72

Explanation:

Given information

2/3 of a number is 2 more than (1/2) of another number

Sum = 129

Set variables

Let x be the first number

Let y be the other number

Set system of equations

[tex]1)~\dfrac{2}{3} x=\dfrac{1}{2} y+2[/tex]

[tex]2)~x + y=129[/tex]

Eliminate fractions in the 1) equation

[tex]\dfrac{2}{3} x\times6=\dfrac{1}{2} y\times6+2\times6[/tex]

[tex]4x=3y+12[/tex]

Move x and y onto the same side

[tex]4x-3y=12[/tex]

Current System

[tex]1)~4x-3y=12[/tex]

[tex]2)~x + y=129[/tex]

Multiply 3 on both sides in 2) equation

[tex]x\times3 + y\times3=129\times3[/tex]

[tex]3x+3y=387[/tex]

Current System

[tex]1)~4x-3y=12[/tex]

[tex]2)~3x+3y=387[/tex]

Add 1) equation and 2) equation together

[tex](4x - 3y)+(3x+3y)=(12)+(387)[/tex]

Expand parenthesis and combine like terms

[tex]4x - 3y + 3x + 3y = 12 + 387[/tex]

[tex]4x + 3x - 3y + 3y=399[/tex]

[tex]7x=399[/tex]

Divide 7 on both sides

[tex]7x\div7=399\div7[/tex]

[tex]\Large\boxed{x=57}[/tex]

Substitute the x value into one of the equations to find the y value

x + y = 129

(57) + y = 129

y = 129 - 57

[tex]\Large\boxed{y=72}[/tex]

Hope this helps!! :)

Please let me know if you have any questions


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The sociological imagination enables us to take into account how individuals, in the welter of their daily experience, often become falsely conscious of their position.

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Economic theory describes the relationship between inflation and unemployment as inverse relationship.

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We can measure the profit earned by a firm in a perfectly competitive industry as Marginal Revenue.

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Bhat and Cho do business as Data Security, a partnership. In most states, for the purposes of collecting judgments and having accounting performed, this firm would be treated as

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The fact that the business that Bhat and Cho do as Data Security, means that for the purpose of collecting judgements and having accounting performed, most states would treat the firm as an independent entity.

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An independent entity is one that does not get counted along with the assets of its owners or partners. In other words, it is independent of the affairs of its owners and is treated as having its own identity.

In this case, the Data Security partnership that Bhat and Cho have will be treated as a separate entity from them which makes it an independent entity.

This is purely for the purpose of collecting judgement and having proper accounting records kept. And even at that, not all states in the United States will require this.

In conclusion, this is an independent entity.

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The Retained earnings account has a credit balance of $50,000 before closing entries are made. Services revenue for the period is $68,200, wages expense is $46,300, and dividends are $14,200. What is the correct closing entry for the expense accounts

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The correct closing entry for the expense accounts will be Debit Revenue accounts $68,200; credit Income Summary $68,200.

At the conclusion of an accounting period, a closure entry is performed to move balances from a temporary account to a permanent account.

Companies use closure entries to reset temporary accounts, which show balances for a particular accounting period, to zero. In doing so, the company transforms these balances into accounts that will always be present on the balance sheet. These continuous accounts show a business's past financial data.

An illustration of a closing entry is when you add up all the revenue and expense account totals at the end of an accounting period to an income summary account, which effectively makes the account balance in the income summary account the net profit or loss for the period. Then, you shift the balance to the retained earnings account from the income summary account.

The net income or loss for the period is accumulated in the retained earnings account, and the temporary account balances are reset to zero so they can be used once more to store period-specific amounts in the following accounting period.

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Capitalism is a system that may be seen as the economic equivalent of?

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Capitalism is a system that may be seen as the economic equivalent of classical liberalism. Which of these philosophers had the greatest impact on Founding Fathers John Locke

Capitalism, also known as the free market economy or free enterprise economy, has been the dominant economic system in the Western world since the fall of feudalism, in which most means of production are privately owned, production is directed, and income is primarily distributed through the functioning of the market

Capitalism often involves private actors owning and managing property according to their own interests, with demand and supply freely priced in the market to serve the best interests of society It comes to be regarded as an economic system. An essential feature of capitalism is the motive for making profits.

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Diseconomies of scale occur when long run average total cost grows as output increases, while constant returns to scale occur when costs remain constant as product increases.  Economies of scale exist when long run average total cost drops as output increases.

The phenomenon known as economies of scale occurs when the scale or magnitude of the production product by a firm increases while the average cost per unit of output decreases. This is an illustration of a natural monopoly, in which there is only one effective number of businesses.

A complex product like an automobile is produced using another form of scale economies.

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The full-time job not worked by a college student (and the wages not earned) because she has to spend a lot of time studying is an example of?

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The full-time job not worked by a college student (and the wages not earned) because she has to spend a lot of time studying is an example of opportunity cost.

Opportunity cost is the time you spend studying and the money you spend doing something else. The farmer decided to plant wheat. The opportunity cost is to grow another crop or use resources (land and farm tools) in another way. Commuters commute by train instead of by car.

Opportunity cost is what you have to give up to buy what you want in other goods and services. When economists use the word cost, they usually mean opportunity cost. The word “expenses” is often used in everyday conversation and news.

Opportunity cost is an economic term that refers to the value of something you have to give up in order to choose something else. In short, it's the value of the path it didn't take.

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Economists who focus on fiscal austerity tend not to be concerned about recessions that may result from fiscal austerity.
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b) false

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Economists who recognition on economic austerity tend now not to be worried approximately recessions that can result from fiscal austerity. B) False

Austerity additionally referred to as austerity measures, is a set of monetary guidelines, normally inclusive of tax increases, spending cuts, or a combination of the two, used by governments to lessen financial deficits.

Austerity implies a reduction in authorities' spending during a duration of vulnerable monetary increase. it is a deflationary financial coverage, related to decreasing fees of monetary boom and better unemployment.

Policies which can be taken into consideration austerity measures include growth in taxes, cutting again on authorities' applications, such as healthcare offerings and useful resources to veterans, a reduction in pensions, and a reduction in salaries and wages for authorities personnel.

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When creating your résumé, you should _____. a. tailor it to the needs of the employer b. use industry and job related terms c. match it to the job description d. all of the above please select the best answer from the choices provided a b c d

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The principle to follow for forming a marketable resume stands D. all of the above.

What is a resume?

A resume exists as a formal document that a job application forms to itemize their capabilities for a position. A resume is usually accompanied by a customized cover letter in which the applicant represents an interest in a characteristic job or company and draws attention to the most relevant specifics on the resume.

A resume exists as a CV (Curriculum Vitae) or a document produced and operated by an individual seeking employment or an appointment to present their:

BackgroundSkillsAccomplishments.

To play a successful resume, one should:

Tailor it to the requirements of the employer.Usage industry and job-related terms.Compare it to the job description.

The principle to follow for forming a marketable resume stands D. all of the above.

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please help this is a math question about geometry !!!! please view the attached images to see the question and the answer choices i am going to give 13 points and a brainlist thank you in your own word what is military courtesy What three questions would a visionary organization seek to answer? multiple select question. how long will it take? why does it exist? why should it do it? what will it do? how will it do it? Step 3 of 6 : find the estimated value of y when x=30. round your answer to three decimal places 4. Throughout life, most people will experience many different parts of the employment process. Examine and explain the steps that occur in the early stages of employment, such as the steps in the job application process (including references and proper documentation), and how one might prepare for explaining gaps in employment in a job interview. A glass inform of frustrum of cone help now look at the picture For disability income insurance purposes, ______ means that a proportionate benefit is paid to an insured whose earned income is reduced because of a disability. A) accidental disability B) residual disability C) temporary disability D) nonoccupational disability What biome do you live in? Describe at least three biotic and three abiotic factors of your biome. A cereal box filling machine is designed to release an amount of 16 ounces of cereal into each box, and the machines manufacturer wants to know of any departure from this setting. The engineers at the factory randomly sample 150 boxes of cereal and find a sample mean of 15.75 ounces. If we know from previous research that the population is normally distributed with a standard deviation of 1.46 ounces, is there evidence that the mean amount of cereal in each box is different from 16 ounces at 0.05 significance? State the hypotheses, list and check the conditions, calculate the test statistic, find the p-value, and make a conclusion in a complete sentence related to the scenario. Members of the senate were not granted enough power within the government. a. true b. false To restore the balance between private and public goods, producers could be required to bear the full? The passage of the civil rights act of 1964 marked the realization of the main goals of the. 11/6 + -2/5 +-13/10? Thirty-two percent of workers in Troberca City are college graduates. You randomly select 50 workers and ask them is he or she is acollege graduate. Find the probability that less than 18 workers are college graduate. (Approximating a Binomial Distribution)(A) 32.6%B 67.4%64.0%36.0% In gluconeogenesis, organisms use atp to make glucose, then in cellular respiration they break down the glucose again to get energy. why not just store the atp? (select all that apply. ) Which term describes a sphere that has the same surface area as the earth's spheroid? Stellar nurseries, such as the orion nebula, contain hundreds or more fragmenting and contracting regions, as well as many protostars and stars. What condition would allow a protostar to become a stable star?. What are the periods in which a grandfather clock, a quartz watch, and an optical clock mark time? (3 points) Given the function h(x) = x 10x + 21, determine the average rate of change of the function over the interval -1 x 10.