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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 4: Q. 553 (page 558)

Shopping. Tula has $\(20$ to spend at the used book sale. Hardcover books cost $\) 2$ each and paperback books cost $$ 0.50$ each. If $x$ is the number of hardcover books Tula can buy and $y$ is the number of paperback books she can buy, the inequality $2 x + \frac{1}{2} y 鈮� 20$ models the situation.
a. Graph the inequality.
b. List three solutions to the inequality $2 x + \frac{1}{2} y 鈮� 20$ where both $x$ and $y$ are whole numbers.

Short Answer

Expert verified

a. The graph of the linear inequality $2 x + \frac{1}{2} y 鈮� 20$ is,

b. The three solutions to the inequality $2 x + \frac{1}{2} y 鈮� 20$ where both $x$ and $y$ are whole numbers are, $(0, 0), (0, 10)$ and $(10, 0)$ .

Step by step solution

01

Part a Step 1. Given information

$2 x + \frac{1}{2} y 鈮� 20$

We need to draw a graph for the given inequality.

02

Part a Step 2. Draw a graph for the given linear inequality.

03

Part b Step 1. Substitute the values of the coordinate 0,0 in the given inequality.

$2 x + \frac{1}{2} y 鈮� 20 2 (0) + \frac{1}{2} (0) 鈮� 20 0 鈮� 20$

which is true.

Therefore, $(0, 0)$ is a solution to $2 x + \frac{1}{2} y 鈮� 20$ .

Substitute the values of the coordinate $(0, 10)$ in the given inequality.

$2 (0) + \frac{1}{2} (10) 鈮� 20 5 鈮� 20$

which is true.

Therefore, $(0, 10)$ is a solution to $2 x + \frac{1}{2} y 鈮� 20$ .

04

Part b Step 2. Substitute the value of coordinate 10,0 in the given inequality.

$2 (10) + \frac{1}{2} (0) 鈮� 20 20 鈮� 20$

which is true.

Therefore, $(10, 0)$ is a solution to $2 x + \frac{1}{2} y 鈮� 20$ .

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