# 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.

Question
Ratios, rates, proportions
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.

2021-03-07
Since 1 ft=12im, then 33ft=396in. Hence, 33ft 9in = 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: $$\displaystyle{P}\to{3}{\left({27}\right)}={81}$$ inches or 6 ft 9in
$$\displaystyle{Q}\to{5}{\left({27}\right)}={135}$$ inches or 11 ft 3 in
$$\displaystyle{R}\to{7}{\left({27}\right)}={189}$$inches or 15 ft 9 in

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