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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A manager has the ability to alter all production elements over the long run .

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The concept of the factors of production, which describes the components required to generate a thing or service for sale, is crucial in economics. Land, labor, capital, and entrepreneurship are the four categories that they are frequently divided into. The two main components of production, however, are occasionally referred to as labor and capital by critics. One or more production aspects may be more crucial than others depending on the particular conditions.

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A time frame in which all cost and production parameters are erratic is known as the long run. Long-term cost adjustments are possible for businesses, although short-term pricing changes can only be influenced by changes in production levels.

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Although licensing is a method of beginning international business, many firms view it as a limitation rather than an opportunity because?

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International licensing is a foreign market entry mode which presents many disadvantages and reasons why companies do not use it as opportunity but sees it as a limitation because there is:

Lower level of income  in this mode than in other entry modes.

Risk of having the reputation and trademark ruined by an incompetent partner

Loss of control of the licensee manufacture and marketing operations and practices which leads to the loss of quality.

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What are liquidated damages the buyer must pay to the seller if the buyer wrongfully fails to sign a release of earnest money to the seller under paragraph 18 of the One to Four Family Residential Contract

Answers

If a buyer wrongfully fails to sign a release of earnest money to the seller, the liquidated damages that the buyer will pay are A) Damages, earnest money, reasonable attorney's fees, and all costs of suit

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The Liquidated damages the buyer must pay to the seller if the buyer wrongfully fails to sign a release of earnest money to the seller under paragraph 18 of the One to Four Family Residential Contract are Damages, earnest money, reasonable attorney's fees, and all costs of suit

This is further explained below.

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Generally, Unliquidated damages are similar to liquidated damages in that they aim to recompense a party that has been affected as a result of a breach of contract; however, unliquidated damages are not monetary in nature. The amount of unliquidated damages, on the other hand, is not calculated in advance in the same way as the number of liquidated damages is when the contract is signed.

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A)Damages, earnest money, reasonable attorney's fees, and all costs of suit

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False is the answer.

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How does a maryland broker’s license renewal differ from a salesperson’s license renewal?

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melanie is currently enrolled in an hmo mapd, and she is talking to sales agent brenda about enrolling in a medicare supplement insurance plan. what should brenda tell melanie

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Brenda should tell Melanie that "Enrolling in a Medicare Supplement Insurance Plan does not automatically disenroll you from your HMO MAPD (Medicare Advantage Prescription Drug) plan.

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A decrease in the supply of money will lead to a(n) _______ in equilibrium real gdp and a(n) _______ in equilibrium price level.

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A decrease in the supply of money will lead to a decrease in equilibrium real GDP and an increase in equilibrium price level.

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Although they represent a relatively small proportion of new companies, most venture capital and a substantial proportion of job creation can be attributed to:________.

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Although they represent a relatively small proportion of new companies, most venture capital and a substantial proportion of job creation can be attributed to: innovation-driven enterprise.

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Job creation can be defined as the way making job available or creating job which inturn lead to employment opportunities for those that are unemployed.

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To maximize total revenue, a firm should ________ its prices it faces elastic demand, and it should ________ its prices if it faces inelastic demand

Answers

To maximize total revenue, a firm should Decrease its prices if it faces elastic demand, and it should increase its prices if it faces inelastic demand

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The price elasticity of demand for a good is a measurement of how sensitive the amount sought is to its price. When the price of a good rises, the amount demanded reduces for almost all of them, but it falls more for some than others.

Price inelasticity is extremely advantageous to organizations and is critical in understanding how to design their pricing strategy. Price inelasticity provides enterprises with greater price freedom because the change in demand is virtually the same whether prices grow or decrease.

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Is the value that you calculate in the last question more or less than the total gain for buyers as a group when there is no price ceiling.

Answers

In this case, for buyers as a group, the gain with the ceiling is greater than the gain without a ceiling.

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The imposed maximum price a seller is permitted to charge for a good or service is known as a price ceiling. Price ceilings are often imposed on necessities like food and energy supplies when they become unaffordable for average customers. Price ceilings are typically established by law.

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Correct question:

This table repeats the buyer values and seller costs. In a market with no restrictions on prices, the total gain captured by buyers and sellers will be $66, with $33 in gain for sellers and $33 in gain for buyers. (You can calculate these values by figuring out who trades at the equilibrium price and calculating how much gain each of them captures.)

With a price ceiling of $8.50, fewer trades will take place. The total gain for buyers and sellers will be lower, although as you will see, it is uncertain exactly how much lower. These problems show you why the gain is uncertain. They also encourage you to think about the following question: Who wins and who loses when there is a price ceiling? If you were representing the interests of all buyers, would you be in favor of a price ceiling?

Buyers V Seller Seller Cost

1 $16 1 $4

2 $15.50 2 $4.50

3 $15 3 $5

4 $14 4 $6

5 $13.50 5 $6.50

6 $13 6 $7

7 $12.50 7 $7.50

8 $12 8 $8

9 $11 9 $9

10 $10.50 10 $9.50

11 $10 11 $10

12 $9.50 12 $10.50

Is the value that you calculated in the last question more or less than the total gain for buyers as a group when there is no price ceiling?

A. In this case, for buyers as a group, the gain with the ceiling is greater than the gain without a ceiling.

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Answers

The inventory loss is around 4%.

The National Restaurant Group is a business association in the restaurant sector that represents over 380,000 restaurant outlets in the United States. The National Restaurant Association Educational Foundation is also run by it. The organization was created in 1919 and is based in Washington, D.C.

Due to pilferage and theft, an ordinary fine-dining restaurant might lose up to five crores in five years. Internal thefts increase the restaurant's food expenses, thus the restaurateur suffers the same amount twice: first when the employee steals it and again when he or she has to pay up the loss from the restaurant's revenues.

According to a National Restaurant Association report, theft accounts for an average of 4% of a restaurant's food expenditures.

Therefore, the answer is 4%.

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When retained earnings are not enough to meet their long-term funding needs, businesses may be able to raise funds by?

Answers

When retained earnings are not enough to meet their long-term funding needs, businesses may be able to raise funds by selling common stock. Long-term funding can be defined as any financial tool with maturity going beyond one year (such as bank loans, bonds, leasing and other forms of debt finance), and public and private equity instruments.

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Retained earnings are the total of profit an establishment has left over after paying all its direct costs, indirect costs, income taxes and its dividends to shareholders.

Therefore, the correct answer is as given above

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Do you think organizations should adopt a single project management methodology for all their projects? why or why not?

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Projects might be of any size or shape. They can range from being quite straightforward and requiring little time and effort to being intricate, multifaceted operations involving sizable teams, joint partnerships, and substantial sums of money.

Choosing the best project management approach is the only way to make sure everything is in order and that you have considered everything.

This post focuses on introducing the most popular project management approaches available and ultimately assisting you in making the best decision possible.

Before going any further, though, let's take a step back and examine what the term "methodology" truly means and how it may be used to carry out project management more effectively.

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In present value calculations, the process of determining the present value of a single sum of money is called:____.
a. pricing.
b. discounting.
c. allocating. n
d. egotiating.

Answers

In present value calculations, the process of determining the present value of a single sum of money is called negotiating.

Negotiation is the dialogue between two or more persons or parties to reach a beneficial outcome on one or more disputed issues. It is an interaction between entities trying to come to an agreement on common interests. A contract may be beneficial to all or some of the parties involved.

Negotiation is a strategic discussion to resolve a problem in a way acceptable to both parties. In negotiations, each party tries to persuade the other to share their point of view. Through negotiation, all parties try to avoid conflict, but agree to compromise in some way.

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When ______ reproduction occurs in a one-celled organism, the organism replicates its dna and splits into two genetically identical cells. Which word describes their measures? linear congruent complementary supplementary How can we explain how the U.S. government and state governments could endorse institutional racism? OR Why do you think this was allowed to happen? Calculate the volume in litres (L) of 1.41 mol of gas at 68.0 kPa and 27.00 C (gas constant R = 8.314 J mol K-.).1. 664 L2. 0.384L3. 51.7L4. 4.66L5. 0.511L evaluate the expression: 7 - 3 + 9 x 8 2 The diameter of a sphere measures 10.4 inches. what is the surface area of the sphere? Barbara runs once around the track in 3 minutes 45 seconds. Liad runs around the track in 2minutes 30 seconds. At these rates, after 10 minutes of running, the distance Barbara has run iswhat fractional part of Liad's? Consequentialism maintains that the rightness of an action is determined by the goodness or badness of relevant? The miranda warning insures that the criminal suspects understand their constitutional rights relating to:_______ a. search and seizure. b. self incrimination. c. having a jury trial. d. double jeopardy. A meson when at rest decays 2 s after it is created. If moving in the laboratory at 0. 99C. Its lifetime according to laboratory clocks would be? Business support systems ____. Data analysis indicated differences between the experimental and control groups at a probability value of. 05 with d =. 15. these results indicate:____. A driver purchased a new automobile from a car dealer. Within a few days of the purchase, the driver returned the car to the dealer for repairs because the car kept pulling to the left whenever the driver applied the brakes. The dealer's mechanic readjusted the brakes but did not detect any other problem with the brake system. The dealer's mechanic assured the driver that the brakes were fixed and, even if they did pull the car to the left again, the brakes would still allow the car to stop.The car worked fine for two days, but then the brakes started pulling to the left again. As the driver was driving the car back to the dealer's shop for further repair, he saw a pedestrian crossing the street. The driver pressed his foot down on the brake pedal, but the master cylinder failed, and the car would not stop. The driver's car struck the pedestrian, injuring him.If the pedestrian sues the driver for his injuries:_________A. The pedestrian will prevail, because the driver knew that there was a problem with his brakes.B. The pedestrian will prevail, because drivers have a duty to maintain their vehicles in safe working order.C. The driver will prevail, because he had no reason to know that his brakes would not stop the car.D. The driver will prevail, because he diligently had his brakes repaired. write a careful description of a metal or an alloy . Use the correct scientific terms.Explain which properties of metals are particularly suited to the function it has. a) The name of the instrument/ things /apparatus b) i) If you choose an alloy: please states the name of all the metals that are consistedin that alloyii) If you choose a single type of metal: Please state the metal.c) Please include explanation in no:2 The example of properties are sonorous,malleable and so on..d) please include descriptions that can fit atleast 2 slides, thank you and have a great/blessing day! Using the molecular data, make a general statement which compares the "rabbit-whale" relationship to the "dog-pig" relationship. Does the cladogram agree with this statement? Explain your reasoning 4.Find the perimeter of the triangle.A. 294 mB. 119 mC. 84 mD. 168 m What type of function is f(x) = 2 log5(3x)? exponential logarithmic polynomial rational A necklace calls for red, blue and white beads in the ratio of 5: 8:12. Ming has used350 beads, how many of them are white in colour? A bacteria culture starts with 260 bacteria and grows at a rate proportional to its size. After 3 hours there will be 780 bacteria. (a) Express the population after t hours as a function of t.population: ? (function of t) (b) What will be the population after 3 hours? (c) How long will it take for the population to reach 1870 ? Key areas you as a broker/agent have control over and impact upon regarding Star Ratings for quality are