Question

A 21-foot rope is cut into 2 pieces. Seven less than three times the length of the longer rope piece x is five times the length of the shorter piece, which is (21 − x) ft. Find the length of the longer rope piece x In ft

Answer 1

The length of the longer rope piece is 14 ft

Explanation:

Let

x -----> the longer piece

y ----> the shorter piece

we know that

The sum of the longer piece plus the shorter piece must be equal to the length of the original piece

x+y=21

y=(21-x) -----> equation A

3x-7=5y ----> equation B

substitute equation A in equation B and solve for x

`3x-7=5(21-x)\\3x-7=105-5x\\5x+3x=105+7\\8x=112\\x=14\ ft`

therefore

The length of the longer rope piece is 14 ft