Question

to achieve the maximum benefit for the heart when exercising, the heart rate (in beats per minute) should be in the target heart - rate zone. the lower limit of this zone is found by taking 70% of the difference between 220 and the age of the person. the upper limit is found by using 85% of the difference. complete parts a through d.
a. find formulas for the upper and lower limits (u and l) as linear equations involving the age x. u = 198 - 0.90x (use integers or decimals for any numbers in the equation. do not factor.)

Explanation:

Step1: Determine upper - limit formula

The upper limit $U$ is found using 85% of the difference. The difference between 220 and the age $x$ is $(220 - x)$. So, $U=0.85(220 - x)=187-0.85x$.

Step2: Determine lower - limit formula

The lower limit $L$ is found using 70% of the difference. The difference between 220 and the age $x$ is $(220 - x)$. So, $L = 0.7(220 - x)=154 - 0.7x$.

Answer:

The formula for the upper limit is $U = 187-0.85x$ and the formula for the lower limit is $L=154 - 0.7x$