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 = 187 - 0.85x (use integers or decimals for any numbers in the equation. do not factor.)
l = 154 - 0.7x (use integers or decimals for any numbers in the equation. do not factor.)
b. what is the target heart - rate zone for a 20 - year - old?
for a 20 - year - old person, the lower limit is (square) and the upper limit is (square) beats per minute.

Explanation:

Step1: Identify the age value

The age $x = 20$

Step2: Calculate the lower - limit L

Given $L=154 - 0.7x$, substitute $x = 20$ into the formula.
$L=154-0.7\times20=154 - 14=140$

Step3: Calculate the upper - limit U

Given $U = 187-0.85x$, substitute $x = 20$ into the formula.
$U=187-0.85\times20=187 - 17=170$

Answer:

The lower limit is 140 and the upper limit is 170 beats per minute.