Ratio Word Problem

Question

A rope is cut in two in the ratio 3.5: 1.75. The difference between the lengths of the ropes is 94.5 inches. What was the original length of the rope?

Answer 1

The ratios of 3.5:1.75 give you a 5.25 total so the ratios of each is

3.5/5.25 = 2/3 and

1.75/5.25 = 1/3

So, if R = the total length of the rope, then

(2/3)R - (1/3)R = 94.5

Solving for R we find that R = 283.5 inches