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Chapter 5: Q. 316 (page 673)

Jake does not want to spend more than \(50on bags of fertilizer and peat moss for his garden.

Fertilizer costs \)2a bag and peat moss costs $5a bag. Jake鈥檚 van can hold at most 20bags.

鈸� Write a system of inequalities to model this situation.

鈸� Graph the system.

鈸� Can he buy 15bags of fertilizer and 4bags of peat moss?

鈸� Can he buy 10bags of fertilizer and 10bags of peat moss?

Short Answer

Expert verified

Part 鈸� System of inequalities to model this situation is: f+p鈮�202f+5p鈮�50

Part 鈸� Graph of the system of inequalities:

鈸� Jake can buy 15bags of fertilizer and 4bags of peat moss.

鈸� Jake cannot buy 10bags of fertilizer and 10bags of peat moss.

Step by step solution

01

Part (a) Step 1. Finding the system of inequalities 

Let, fbe the number of bags of fertilizer and pbe the number of bags of peat moss.

Jake wants to buy fertilizer and peat moss for his garden and his van can hold at most 20bags. So, the inequality is: f+p鈮�20.

Fertilizer costs $2a bag, peat moss costs $5a bag and Jake does not want to spend more than $50. So, the inequality is: 2f+5p鈮�50.

The system of inequalities is:f+p鈮�202f+5p鈮�50

02

Part (b) Step 1. Graphing the system of inequalities  

Below is the graph of the system of inequalities:f+p鈮�202f+5p鈮�50

03

Part (c) Step 1. Finding whether Jake can buy 15 bags of fertilizer and 4 bags of peat moss

As the point (15,4)is in the double shaded region of the graph, so, Jake can buy 15bags of fertilizer and4 bags of peat moss.

04

Part (d) Step 1. Finding whether Jake can buy 10 bags of fertilizer and 10 bags of peat moss

As the point (10,10)is not in the double shaded region of the graph, so, Jake cannot buy 10bags of fertilizer and10 bags of peat moss.

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