# Heart Rate Formula

• MHB
• mathland
In summary, the exercise target heart rate region can be represented by the inequalities 110 - 0.50x ≤ y ≤ 187 - 0.85x, where x represents a person's age in years and y represents their target heart rate in beats per minute. This means that for a person between 20 and 70 years old, their target heart rate should be between 110 - 0.50x and 187 - 0.85x beats per minute. To find two solutions, we can plug in different values of x, such as 20 and 70, and interpret the resulting y values as the target heart rate for those ages. For a 20-year-old, the target heart rate would be

#### 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?

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

-Dan

topsquark said:
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

mathland said:
(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