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 .

Previous
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. 2OECh. 3.8 - Prob. 3OECh. 3.8 - Prob. 1WECh. 3.8 - Prob. 2WECh. 3.8 - Prob. 3WECh. 3.8 - Prob. 4WECh. 3.8 - Prob. 5WECh. 3.8 - Prob. 6WECh. 3.8 - Prob. 7WECh. 3.8 - Prob. 8WECh. 3.8 - Prob. 9WECh. 3.8 - Prob. 10WECh. 3.8 - Prob. 11WECh. 3.8 - Prob. 1MRECh. 3.8 - Prob. 2MRECh. 3.8 - Prob. 3MRECh. 3.8 - Prob. 4MRECh. 3.8 - Prob. 5MRECh. 3.8 - Prob. 6MRECh. 3.8 - Prob. 7MRECh. 3.8 - Prob. 8MRECh. 3.8 - Prob. 9MRECh. 3.8 - Prob. 10MRECh. 3.8 - Prob. 11MRECh. 3.8 - Prob. 12MRECh. 3.8 - Prob. 1STCh. 3.8 - Prob. 2STCh. 3.8 - Prob. 3STCh. 3 - Prob. 1CRCh. 3 - Prob. 2CRCh. 3 - Prob. 3CRCh. 3 - Prob. 4CRCh. 3 - Prob. 5CRCh. 3 - Prob. 6CRCh. 3 - Prob. 7CRCh. 3 - Prob. 8CRCh. 3 - Prob. 9CRCh. 3 - Prob. 10CRCh. 3 - Prob. 11CRCh. 3 - Prob. 12CRCh. 3 - Prob. 1CTCh. 3 - Prob. 2CTCh. 3 - Prob. 3CTCh. 3 - Prob. 4CTCh. 3 - Prob. 5CTCh. 3 - Prob. 6CTCh. 3 - Prob. 7CTCh. 3 - Prob. 8CTCh. 3 - Prob. 9CTCh. 3 - Prob. 10CTCh. 3 - Prob. 11CTCh. 3 - Prob. 12CTCh. 3 - Prob. 13CTCh. 3 - Prob. 14CTCh. 3 - Prob. 15CTCh. 3 - 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