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 person? the lower limit is 140 and the upper limit is 170 beats per minute.
c. what is the target heart - rate zone for a 40 - year - old person? the lower limit is and the upper limit is beats per minute.

Explanation:

Step1: Identify the formulas

The lower - limit formula is $L = 154-0.7x$ and the upper - limit formula is $U = 187 - 0.85x$, where $x$ is the age of the person.

Step2: Solve for part b (20 - year - old)

Substitute $x = 20$ into the lower - limit formula:
$L=154−0.7\times20=154 - 14=140$
Substitute $x = 20$ into the upper - limit formula:
$U=187−0.85\times20=187 - 17 = 170$

Step3: Solve for part c (40 - year - old)

Substitute $x = 40$ into the lower - limit formula:
$L=154−0.7\times40=154 - 28 = 126$
Substitute $x = 40$ into the upper - limit formula:
$U=187−0.85\times40=187 - 34=153$

Answer:

For a 40 - year - old person, the lower limit is 126 and the upper limit is 153 beats per minute.