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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≤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≤24

02

Step 2. Solve fory.

Solve for yin terms of x.

2x+3y−2x≤24−2x3y3≤24−2x3y≤8−23x

03

Step 3. Select a test point.

Let (0,0)be a test point. Substitute 0 for xand 0 for yinto y≤8−23x.

0≤8−23(0)0≤8

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

04

Step 4. Graph an inequality.

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

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Most popular questions from this chapter

Write an inequality that best represents the graph.

A sporting goods company near the beach rents bicycles for \(10 plus \)5per hour. Write an equation in slope-intercept form that shows the total cost,yof renting a bicycle for xhours. How much would it cost Emily to rent a bicycle for 6 hours?

Record your answers on the answer sheet provided by your teacher or on a sheet of paper.

Question: Solve−4<3x+8≤23

State whether each sentence is true or false. If false, replace the underlined term to make a true sentence.

The boundary is the graph of the equation of the line that defines the edge of each half-plane.

State whether each sentence is true or false. If false, replace the underlined term to make a true sentence.

Set-builder notation is a less concise way of writing a solution set.
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