A piece of ribbon 3600 cm long is cut into 3 parts, A, B and C.
A is 3 times as long as B.
C is 180 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 + 180
Length of A = 3 x (1 u + 180) = 3 u + 540

Total length of A, B and C
= 3 u + 540 + 1 u + 180 + 1 u
= 3 u + 1 u + 1 u + 540 + 180
= 5 u + 720

5 u + 720 = 3600
5 u = 3600 - 720
5 u = 2880

1 u = 2880 ÷ 5 = 576

Length of A longer than B
= 3 u + 540 - (1 u + 180)
= 3 u - 1 u + 540 - 180
= 2 u + 360
= 2 x 576 + 360
= 1152 + 360
= 1512 cm

(b)
Total length of A and C
= 3 u + 540 + 1 u
= 4 u + 540
= 4 x 576 + 540
= 2304 + 540
= 2844 cm

Answer(s): (a) 1512 cm; (b) 2844 cm