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 1.7, Problem 3ST

To determine

Translate given statement into an equation and find the length of each pieces of rope.

Expert Solution & Answer

Answer to Problem 3ST

Required equation x+2x+2=11 .

The lengths of the piece of rope are 3 ft and 8 ft.

Explanation of Solution

Given information:

Total length of a rope = 11 ft.

One piece is 2 ft longer than twice the other piece.

Calculation:

Let, the length of smaller piece of rope = x

Twice of x = 2x.

Then the length of larger piece of rope (2 ft more than twice of x ) = 2x+2 ft

Total length of rope = 11 ft.

Sum of smaller piece and larger piece = total length of rope.

x+2x+2=11

Combine like terms

3x+2=11

Subtract 2 on both sides

3x+2−2=11−2⇒3x=9

Divide by 3 on both sides

3x3=93⇒x=3

Therefore, the length of smaller piece of rope= 3 ft.

And the length of larger piece of rope = 2x+2=2(3)+2=8 ft.

Chapter 1.7, Problem 2ST

Chapter 1.7, Problem 4ST

Chapter 1 Solutions

Algebra: Structure And Method, Book 1

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