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Contemporary Mathematics for Busin...

8th Edition
Robert Brechner + 1 other
ISBN: 9781305585447

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Chapter
Section
BuyFindarrow_forward

Contemporary Mathematics for Busin...

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

Set up and solve equations for the following business situations.

An estate is to be distributed among a wife, three children, and two grandchildren. The children will each receive three times as much as each grandchild, and the wife will receive four times as much as each child. If the estate amounts to $115,000, how much will each person receive?

To determine

To calculate: The amount received by each person, if the estate amount $115,000 is distributed among a wife, three children, and two grandchildren. The children receive three times as each grandchild and the wife receive four times the child.

Explanation

Given Information:

The estate amount $115,000 is distributed among a wife, three children, and two grandchildren. The children receive three times as each grandchild and the wife receive four times the child.

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 receive by grandchild plus amount receive by child plus amount receive by wife equals estate amount, $115,000.

Suppose that amount received by grandchild is X.

Consider the people, a wife, three children, and two grandchildren,

Consider the children receive three times as each grandchild, 3X.

Also consider the wife receives four times as child, 4(3X).

Also consider total estate amount, 2X+3(3X)+4(3X)=$115,000.

Now solve the equation,

2X+3(3X)+4(3X)=115,000.

Solve the parenthesis and combine the unknowns on left side,

2X+3(3X)+4(3X)=115,0002X+9X+12X=115,00023X=115000

This equation represents that X is multiplied by 23

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