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Chapter 4: Q. 421 (page 485)

Translate to a system of

inequalities and solve.

Andi wants to spend no more than

\(50 on Halloween treats. She

wants to buy candy bars that cost

\)1 each and lollipops that cost

$0.50 each, and she wants the

number of lollipops to be at least

three times the number of candy

bars.

(a) Write a system of inequalities to

model this situation.

(b) Graph the system.

(c) Can she buy 20 candy bars and

40 lollipops?

Short Answer

Expert verified

(a)x鈮�0y鈮�0x+0.5y鈮�50y鈮�3x

(b)

(c) no

Step by step solution

01

Part (a) Step 1. Given information.

Cost of candy bar $1.

Cost of lollipops $0.05.

Money to be spent 鈮�50$

Number of lollipops is three times the number of candy bars.

02

Part (a) Step 2. Framing equations.

From problem given above following equations can be drawn:

x鈮�0y鈮�0x+0.5y鈮�50......(1)y鈮�3x.........(2)

03

Part (b) Step 1. Given information.

x鈮�0y鈮�0x+0.5y鈮�50y鈮�3x

04

Part (b) Step 2. Drawing the graph.

Constructing the graph using given data:

x鈮�0y鈮�0x+0.5y鈮�50y鈮�3x

05

Part (c) Step 1. Given information.

x鈮�0y鈮�0x+0.5y鈮�50y鈮�3x

No of candy bars = 20

No of Lollipops = 40

06

Part (c) Step 2. Calculation.

Substituting the values of candy bars and lollipops we get:

x+0.5y鈮�5020+0.5(40)=40and40鈮�50Whichsatisfiestheaboveinequality.Now,letscheckforanotherinequalityy鈮�3x40鈮�3(20)40鈮�60Whichdoesnotholds.

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