Question

A ribbon measuring (v+4) feet in length was cut into two pieces in the ratio 3:7 What was the length of the longer piece

Answer 1

Let n be the common factor between the two pieces. Then, the length of each piece is given by 3n and 7n, respectively. The length of the longer piece would be 7n/v+4 So:

3n+7n=v+4
3n+7n/v+4=1
3n/v+4 +7n/v+4=1
7n/v+4=1-3n/v+4

Answer 2

You started well.

Ok, up to 3n+7n = v+4 , you have like terms in n
10n = v+4
n = (v+4)/10

so the longer piece is 7n or
7(v+4)/10
or
(7/10)(v+4)