Question

A 97-foot rope is cut into two pieces so that the longer piece is 5 feet more than three times the smaller piece. What are the lengths of both pieces?

Answer 1

`A = 74`
`B = 23`

Explanation:

This is a problem in which we use the known length and the relationship of the two lengths to form an equation that uses the unknown quantity.

Lengths A and B sum to the total of 97.
If B is the smaller piece, then
`A = 5 + 3B`
Put these together to get:

`A + B = 97` ; `A = 5 + 3B`
`5 + 3B + B = 97` ; `4B + 5 = 97` ; `4B = 92`
`B = 23`
Then: `A = 5 + 3B` ; `A = 5 + 3(23)` ; `A = 74`
CHECK:
`A + B = 97` ; `74 + 23 = 97`; `97 = 97` CORRECT!