   Chapter 5.II, Problem 12RE ### Contemporary Mathematics for Busin...

8th Edition
Robert Brechner + 1 other
ISBN: 9781305585447

#### Solutions

Chapter
Section ### Contemporary Mathematics for Busin...

8th Edition
Robert Brechner + 1 other
ISBN: 9781305585447
Textbook Problem

# Set up and solve equations for the following business situations.You are the administrator of an annual essay contest scholarship fund. This year a $48,000 college scholarship is being divided between the top two contestants so that the winner receives three times as much as the runner-up. How much will each contestant receive? To determine To calculate: The amount received by each contestant, if the scholarship amount$48,000 is distributed among top two contestants. The winner receives three times as runner-up.

Explanation

Given Information:

The scholarship amount $48,000 is distributed among top two contestants. The winner receives three times as runner-up. Formula used: To solve the equation and prove the solution, follow the steps as mentioned below. Step 1: Understand the problem and write the facts of the equation. Step2: List the known and the unknows from the problem. Step3: Write the equation with the help of following table of key word,  Equal Sign Addition Subtraction Multiplication Division Parentheses Is And Less of Divide Times the quantity of Are Added to Less than Multiply Divided by Was Totals Smaller than Times Divided into Equals The sum of Minus Product of Quotient of Gives Plus Difference Multiplied by Ratio of Giving More than Decreased by Twice Leaves Larger than Reduced by Double Results in Increased by Take away Triple Produces Greater than Loss of At yields exceeds Fewer than @ Step4: Solve the equation by rearrange the unknown values to the left side and known values to the right side of the equal sign. Step5: Prove the solution by substituting the value obtained from step 4 in the equation formed in step 4 then check the left and right of the equation if, they are equal then the answer is correct. Calculation: Underline the keyword by using the table of of key word. Amount received by winner plus amount received by runner-up plus equals scholarship amount,$48,000.

Suppose that amount received by runner-up is X.

Consider the winner receives three times as runner-up, 3X.

Also consider total scholarship amount, X+3X=\$48,000

Now solve the equation

X+3X=48,000

Combine the unknowns on left side,

X+3X=48,0004X=48,000

This equation represents that X is multiplied by 4

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