A rope is cut into three pieces P, Q, and R. The lengths of the pieces are in the ratio 3:5:7. If the rope is 33 feet 9 inches long, find the length of P, Q, and R.

Chesley

Chesley

Answered question

2021-03-06

A rope is cut into three pieces P, Q, and R. The lengths of the pieces are in the ratio 3:5:7. If the rope is 33 feet 9 inches long, find the length of P, Q, and R.

Answer & Explanation

ensojadasH

ensojadasH

Skilled2021-03-07Added 100 answers

Since 1ft=12ln, then 33ft=396ln. Hence, 33ft 9ln=405 inches. Using the ratio, let the prices be 3x,5x, and 7x, all in inches.
So, we can write and solve for x: 3x+5x+7x=405
15x=405
x=27
So, the lengths of P,Q and R are: P3(27)=81 inches or 6 ft 9in
Q5(27)=135 inches or 11 ft 3 in
R7(27)=189 inches or 15 ft 9 in

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