MHB What Are the Solutions to the System of Inequalities for Target Heart Rate?

[mathland]

One formula for a person’s maximum heart rate is 220 − x, where x is the person’s age in years for
20 ≤ x ≤ 70. The American Heart Association recommends that when a person exercises, the person should strive for a heart rate that is at least 50% of the maximum and at most 85% of the maximum.

(a) Write a system of inequalities that describes the exercise target heart rate region.

I need someone to get me started here.

(b) Find two solutions of the system and interpret their meanings in the context of the problem.

What exactly is part (b) asking for? Is part (b) asking for the value(s) of x?

 

[topsquark]

Here's a start:
(a) What is 50 percent of 220 - x? What is 85 percent of 220 - x?

-Dan

 

[mathland]

Here's a start:
(a) What is 50 percent of 220 - x? What is 85 percent of 220 - x?

-Dan

(A)0.50(220 - x) = 110 - 0.50x

(B)

0.85(220 - x) = 187 - 0.85x

 

[topsquark]

(A)0.50(220 - x) = 110 - 0.50x

(B)

0.85(220 - x) = 187 - 0.85x

Good! So what's the range of values this could take? (Hint: What's the smallest value of x?)

-Dan