Chapter 5.II, Problem 12RE

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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

Explanation

**Given Information:**

The scholarship amount

**Formula used:**

To solve the equation and prove the solution, follow the steps as mentioned below.

Step

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,

Suppose that amount received by runner-up is *X*.

Consider the winner receives three times as runner-up,

Also consider total scholarship amount,

Now solve the equation

Combine the unknowns on left side,

This equation represents that

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