A piece of ribbon 3200 cm long is cut into 3 parts, A, B and C.
A is 2 times as long as B.
C is 240 cm shorter than B.
Give the answers in cm.

1. How much longer is A than B?
2. What is the total length of A and C?

(a)
Choose the shortest length to be 1 u.

Length of C = 1 u
Length of B = 1 u + 240
Length of A = 2 x (1 u + 240) = 2 u + 480

Total length of A, B and C
= 2 u + 480 + 1 u + 240 + 1 u
= 2 u + 1 u + 1 u + 480 + 240
= 4 u + 720

4 u + 720 = 3200
4 u = 3200 - 720
4 u = 2480

1 u = 2480 ÷ 4 = 620

Length of A longer than B
= 2 u + 480 - (1 u + 240)
= 2 u - 1 u + 480 - 240
= 1 u + 240
= 1 x 620 + 240
= 620 + 240
= 860 cm

(b)
Total length of A and C
= 2 u + 480 + 1 u
= 3 u + 480
= 3 x 620 + 480
= 1860 + 480
= 2340 cm

Answer(s): (a) 860 cm; (b) 2340 cm