Algebra: Structure And Method, Book 1

(REV)00 Edition

ISBN: 9780395977224

Author: Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher: McDougal Littell

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Question

Chapter 3.5, Problem 4ST

To determine

To find: the amount money Hilary, Paul and Jeff have

Expert Solution & Answer

Answer to Problem 4ST

The amount of money Hilary have is $13.5

The amount of money Paul have is $4.5

The amount of money Jeff have is $9.5

Explanation of Solution

Given information: “Hilary has three times as much money as Paul”, “Jeff has $4 less than Hilary and $5 more than Paul”

Concept Involved:

Assign variable for the unknown that we need to find. Use the keywords in the statement to rewrite the statement to meaningful math equation.

“same as” means =

“more than” means +

“less” means −

Solve the equation by getting the variable in one side of the equation and undoing whatever is done to it by performing reverse operation.

Calculation: Let ‘ x’ be the amount of money Paul have

Using the keywords given in the sentence “Hilary has three times as much money as Paul” we can conclude that the amount of money Hilary have is ‘ 3x’

Using the keywords given in the sentence “Jeff has $4 less than Hilary and $5 more than Paul” we can get two expressions to represent the amount of money Jeff have as ‘ 3x-4’ & ‘ x+5’

We can equate the two expressions representing Jeff money

3x−4=x+5

In the process of getting x in one side of the equation subtract on both sides

3x−4−x=x+5−x

Combine like terms on both sides

2x−4=5

Add 4 on both sides of the equation

2x−4+4=5+4

Divide by 3 on both sides of the equation

2x2=92

Simplify fraction on both sides of the equation

x=4.5

Evaluate the value of the expression 3x by substituting 4.5 for x

3(4.5)=13.5

Evaluate the value of the expression x+5 by substituting 4.5 for x

4.5+5=9.5

Conclusion:

The amount of money Hilary is represented by expression 3x and equal to 13.5

The amount of money Paul is represented by expression x and equal to 4.5

The amount of money Jeff is represented by expression x+5 and equal to 9.5

Chapter 3.5, Problem 3ST

Chapter 3.6, Problem 1OE

Chapter 3 Solutions

Algebra: Structure And Method, Book 1

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