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Chapter 5: Q. 318 (page 673)

Juan is studying for his final exams in Chemistry and Algebra. He knows he only has 24hours to study, and it will take him at least three times as long to study for Algebra than Chemistry.

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

鈸� Graph the system.

鈸� Can he spend 4hours on Chemistry and 20hours on Algebra?

鈸� Can he spend 6hours on Chemistry and 18hours on Algebra?

Short Answer

Expert verified

Part 鈸� System of inequalities to model this situation is: c+a鈮�24a鈮�3c

Part 鈸� Graph of the system of inequalities:

鈸� Juan can spend 4hours on Chemistry and 20hours on Algebra.

鈸� Juan can spend 6hours on Chemistry and 18hours on Algebra.

Step by step solution

01

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

Let, cbe the number of hours to study chemistry and abe the number of hours to study algebra for juan.

Juan knows he only has 24 hours to study. So, the inequality is:c+a鈮�24.

It will take him at least three times as long to study for Algebra than Chemistry. So, the inequality is: a鈮�3c.

The system of inequalities is:c+a鈮�24a鈮�3c

02

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

Below is the graph of the system of inequalities: c+a鈮�24a鈮�3c

03

Part (c) Step 1. Finding whether Juan can spend 4 hours on Chemistry and 20 hours on Algebra

As the point (4,20)is in the double shaded region of the graph, so, Juan can spend 4 hours on Chemistry and 20 hours on Algebra.

04

Part (d) Step 1. Finding whether Juan can spend 6 hours on Chemistry and 18 hours on Algebra

As the point (6,18)is in the double shaded region of the graph, so, Juan can spend 6hours on Chemistry and 18 hours on Algebra.

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