Question

the length of rope P is three times the length of rope Q. After 10cm of rope is cut from rope P and rope Q respectively, the length of rope P is four times the length of Q. Calculate the original length, in cm, of rope P before it is cut.

Answer 1

150 cm

Explanation:

The information in the question includes;

The length of rope P = 3 × The length of rope Q

The length of rope P - 10 cm = 4 × (The length of rope Q - 10 cm)

Let p represent the original length of rope P and let q represent the original length of rope Q, we have;

p = 3·q...(1)

p - 10 = 4·(q - 10)...(2)

Expanding equation (2) gives;

p - 10 = 4·q - 40

∴ p = 4·q - 40 + 10 = 4·q - 50

p = 4·q - 50...(3)

Equating the values of p in equation (1) and equation (3) gives;

p = 3·q, and p = 4·q - 50, therefore, by the substitution property of equality, we have;

3·q = 4·q - 50

50 = 4·q - 3·q = q

q = 50

p = 3·q

∴ p = 3 × 50 = 150

The original length of P before it was cut, p = 150 cm.