Question

A tuxedo rental shop rents tuxedos with sleeve lengths from 20 inches to 40 inches. The shop says the length of the sleeves should be about 1.2 times a person's arm length. Write and solve a compound inequality that represents the arm lengths of people the shop does not provide tuxedos for.

Answer 1

Explanation:

Let the arm length of tuxedo be x which varies from 20 inches to 40 inches.

If length of the sleeves is about 1.2 times a person's arm length.

Then the arm length of a person will be 1.2x.

Inequality for the arm length will be

20 < 1.2x < 40

Now we divide this inequality by 1.2

`(20)/(1.2)<x<(40)/(1.2)`

16.67 < x < 33.33

This inequality represents the arm length of people having arm length between 16.67 and 33.33 inches.

tuxedo rental shop does not provide tuxedos to the persons having arm length less than 16.67 and greater than 33.33.

Answer 2

Let the person's arm length be = x

Condition is : sleeve lengths available from 20 inches to 40 inches and the length of the sleeves should be about 1.2 times a person's arm length.

So, the inequality equation becomes:

`20\leq1.2x\leq40`

This gives x=
`(20)/(1.2)=16.66` or
`16(2)/(3)`

or x=
`(40)/(1.2)`=33.33 or
`33(1)/(3)`

Hence, the shop does not provide tuxedos to people with arm length less than 16.66 inches and greater than 33.33 inches.