A piece of ribbon 2300 cm long is cut into 3 parts, B, C and A.
B is 4 times as long as C.
A is 220 cm shorter than C.
Give the answers in cm.

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

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

Length of A = 1 u
Length of C = 1 u + 220
Length of B = 4 x (1 u + 220) = 4 u + 880

Total length of B, C and A
= 4 u + 880 + 1 u + 220 + 1 u
= 4 u + 1 u + 1 u + 880 + 220
= 6 u + 1100

6 u + 1100 = 2300
6 u = 2300 - 1100
6 u = 1200

1 u = 1200 ÷ 6 = 200

Length of B longer than C
= 4 u + 880 - (1 u + 220)
= 4 u - 1 u + 880 - 220
= 3 u + 660
= 3 x 200 + 660
= 600 + 660
= 1260 cm

(b)
Total length of B and A
= 4 u + 880 + 1 u
= 5 u + 880
= 5 x 200 + 880
= 1000 + 880
= 1880 cm

Answer(s): (a) 1260 cm; (b) 1880 cm