Question

A tuxedo rental shop rents tuxedos with sleeve lengths from 19.2 inches to 39.5 inches. The shop says lengths of arms should be about 1.2 times a person's height. Solve the compound inequality to find the actual arm lengths (a) of people the shop provides tuxedos for.

a. a ≤ 19.2 or a ≥ 39.5
b. 1.2h ≤ a ≤ 1.2h
c. 0.83h ≤ a ≤ 1.25h
d. 0.83a ≤ h ≤ 1.25a

Answer 1

To find the actual arm lengths (a) of people the shop provides tuxedos for, use the compound inequality 1.2h ≤ a ≤ 1.2h. Substitute h with the given range of sleeve lengths (19.2 inches to 39.5 inches) multiplied by 1.2 to get the range of arm lengths, which is 23.04 inches to 47.4 inches.

Step-by-step explanation:

To find the actual arm lengths (a) of people the shop provides tuxedos for, we need to use the compound inequality given: 1.2h ≤ a ≤ 1.2h.

In this inequality, h represents a person's height. Since the shop says arm lengths should be about 1.2 times a person's height, we can substitute h with the given range of sleeve lengths (19.2 inches to 39.5 inches) multiplied by 1.2 to get the range of arm lengths.

So, the actual arm lengths (a) of people the shop provides tuxedos for are 23.04 inches to 47.4 inches.