Question

Solving a word problem using a system of linear inequalities

Rita does a weekly exercise program consisting of cardiovascular work and weight training. Each week, she exercises for at
least 11 hours. She spends at most 7 hours on weight training. She spends at most 8 hours doing cardiovascular work. Let y
denote the time (in hours) that Rita spends doing cardiovascular work. Let y denote the time (in hours) that she spends on
weight training. Shade the region corresponding to all values of y and y that satisfy these requirements

Answer 1

Inequalities help us to compare two unequal expressions. The shaded potion can be made as shown below.

What are inequalities?

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

Rita does a weekly exercise program consisting of cardiovascular work and weight training. Each week, she exercises for at least 11 hours. She spends at most 7 hours on weight training. She spends at most 8 hours doing cardiovascular work.

Therefore, For the given condition let x denote the time (in hours) that Rita spends doing cardiovascular work. Let y denote the time (in hours) that she spends on weight training.

Now, the inequalities can be written as,

x + y > 11

x ≤ 7

y ≤ 8

Hence, the shaded potion can be made as shown below.

Learn more about Inequality:

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