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Chapter 5: Q53. (page 324)

BAKERY Ben has $24 to spend on cookies and cupcakes. Write and graph an inequality that represents what Ben can buy.

Short Answer

Expert verified

A graph of a given inequality is

The inequality is2x+3y鈮�24.

Step by step solution

01

Step 1. Write given information in the form of inequality.

Letxbe the number of cookies andybe the number of cupcakes. The cookies are $2 each, therefore, the cost of the cookies is2x.The cupcakes are $3 each, therefore, the cost of cupcakes is3y. As the Ben can spend no more than $24, the total cost must be less than or equal to $24. Therefore,

2x+3y鈮�24

02

Step 2. Solve fory.

Solve for yin terms of x.

2x+3y鈭�2x鈮�24鈭�2x3y3鈮�24鈭�2x3y鈮�8鈭�23x

03

Step 3. Select a test point.

Let (0,0)be a test point. Substitute 0 for xand 0 for yinto y鈮�8鈭�23x.

0鈮�8鈭�23(0)0鈮�8

Therefore, the half plane containing the origin is the solution.

04

Step 4. Graph an inequality.

Graph an inequality,2x+3y鈮�24and shade the half plane containing test point.

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