Algebra: Structure And Method, Book 1
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
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Chapter 3.5, Problem 11P
To determine

To find: the numbers based on the given description

Expert Solution & Answer
Check Mark

Answer to Problem 11P

The one number is 8 and the other number is 7 .

Explanation of Solution

Given information: “The sum of two numbers is 15”, “Three times one of the numbers is 11 less than five times the other”

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 =

“less than” means −

“Sum” means +

“three times” means 3×

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 one number

Since the sum of two numbers is 15, the expression that represents the other number is x less than 15.

  15−x

Rewrite the statement “Three times one of the numbers is 11 less than five times the other” in terms of x

3 times x is 11 less than 5 times 15-x

Use the keywords to write the statement “3 times x is 11 less than 5 times 15-x ” as an equation

  3x=5(15−x)−11

Distribute 5 in right side of the equation

  3x=75−5x−11

In the process of getting x in one side of the equation add 5x on both sides

  3x+5x=75−5x−11+5x

Combine like terms on both sides

  8x=64

Divide 8 on both sides of the equation

  8x8=648

Simplify fraction on both sides of the equation

  x=8

Substitute 8 for x in the expression 15−x  to identify the other number

  15−8=7

Conclusion:

The one number is 8 and the other number is 7 .

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Chapter 3.5, Problem 10P
Next
Chapter 3.5, Problem 12P

Chapter 3 Solutions

Algebra: Structure And Method, Book 1

Ch. 3.1 - Prob. 1OECh. 3.1 - Prob. 2OECh. 3.1 - Prob. 3OECh. 3.1 - Prob. 4OECh. 3.1 - Prob. 5OECh. 3.1 - Prob. 6OECh. 3.1 - Prob. 7OECh. 3.1 - Prob. 8OECh. 3.1 - Prob. 9OECh. 3.1 - Prob. 10OE
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Prob. 12MSCh. 3 - Prob. 13MSCh. 3 - Prob. 14MSCh. 3 - Prob. 15MSCh. 3 - Prob. 16MSCh. 3 - Prob. 17MSCh. 3 - Prob. 18MSCh. 3 - Prob. 19MSCh. 3 - Prob. 20MSCh. 3 - Prob. 21MSCh. 3 - Prob. 22MSCh. 3 - Prob. 23MSCh. 3 - Prob. 24MSCh. 3 - Prob. 25MSCh. 3 - Prob. 26MSCh. 3 - Prob. 27MSCh. 3 - Prob. 28MSCh. 3 - Prob. 29MSCh. 3 - Prob. 30MSCh. 3 - Prob. 31MSCh. 3 - Prob. 32MSCh. 3 - Prob. 33MSCh. 3 - Prob. 34MSCh. 3 - Prob. 35MSCh. 3 - Prob. 36MSCh. 3 - Prob. 1MPSCh. 3 - Prob. 2MPSCh. 3 - Prob. 3MPSCh. 3 - Prob. 4MPSCh. 3 - Prob. 5MPSCh. 3 - Prob. 6MPSCh. 3 - Prob. 7MPSCh. 3 - Prob. 8MPSCh. 3 - Prob. 9MPSCh. 3 - Prob. 10MPSCh. 3 - Prob. 11MPSCh. 3 - Prob. 12MPSCh. 3 - Prob. 13MPSCh. 3 - Prob. 14MPSCh. 3 - Prob. 15MPSCh. 3 - Prob. 16MPSCh. 3 - Prob. 17MPS

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