What was the length of the longer piece of ribbon?

Question

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

Answer 1

(v+4)/(3+7)=(v+4)/10

7[(v+4)/10]=(7v+28)/10 is the length of the longer piece

3[(v+4)/10]=(3v+12)/10 is the length of the shorter piece

to check, add them or set up a ratio

(7v+28+3v+12)/10=(10v+40)/10=v+4, or...

3[(v+4)/10]/7[(v+4)/10]=[(3v+12)/10]/[(7v+28)/10]=(3v+12)/(7v+28)=3(v+4)/7(v+4)=3/7 (the 10s cancel !!)