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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Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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Question

Chapter 3.5, Problem 12P

To determine

To find: the numbers based on the given description

Expert Solution & Answer

Answer to Problem 12P

The smaller number is 17 and the larger number is 26 .

Explanation of Solution

Given information: “The difference of two numbers is 9”, “Five times the smaller is 7 more than three times the larger”

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.

“is” means =

“more than” means +

“Difference” means -

“times” 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: Assign variable for the unknown that we need to find

Let x represents smaller number

Since the difference of two numbers is 9, the expression that represents the larger number is x more than 9.

x+9

Rewrite the statement “Five times the smaller is 7 more than three times the larger” in terms of x

5 times x is 7 more than 3 times x+9

Use the keywords to write the statement “Five times the smaller is 7 more than three times the larger” as an equation

5x=7+3(x+9)

Distribute 5 in right side of the equation

5x=7+3x+27

In the process of getting x in one side of the equation subtract 3x on both sides

5x−3x=34+3x−3x

Combine like terms on both sides

2x=34

Divide 2 on both sides of the equation

2x2=342

Simplify fraction on both sides of the equation

x=17

Substitute 17 for x in the expression x+9 to identify the larger number

17+9=26

Conclusion:

The smaller number is 17 and the larger number is 26 .

Chapter 3.5, Problem 11P

Chapter 3.5, Problem 13P

Chapter 3 Solutions

Algebra: Structure And Method, Book 1

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