Compound Inequalities

Question

When you exercise, your pulse rate rises. Recommended pulse rates vary with age and physical condition. For vigorous exercise such as jogging, the inequality 0.7(220 – a) ≤ R ≤ 0.85(220 – a) gives a target range for pulse rate R (in beats per minute), based on age a (in years).

A. What is the target range for pulse rates for 31 years old? Round to the nearest whole number.


B. Your cousin’s target rate is in the range between 140 and 170 beats per minute. What is your cousin’s age?

Answer 1

For question A, substitute 31 for a in the inequality to find the target range

 

For question B, solve 0.7(220 - a) = 140 for a. You could also solve 0.85(220 - a) = 170 for a. Both should yield the same value for a.