A piece of ribbon 4000 cm long is cut into 3 parts, C, A and B.
C is 3 times as long as A.
B is 250 cm shorter than A.
Give the answers in cm.

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

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

Length of B = 1 u
Length of A = 1 u + 250
Length of C = 3 x (1 u + 250) = 3 u + 750

Total length of C, A and B
= 3 u + 750 + 1 u + 250 + 1 u
= 3 u + 1 u + 1 u + 750 + 250
= 5 u + 1000

5 u + 1000 = 4000
5 u = 4000 - 1000
5 u = 3000

1 u = 3000 ÷ 5 = 600

Length of C longer than A
= 3 u + 750 - (1 u + 250)
= 3 u - 1 u + 750 - 250
= 2 u + 500
= 2 x 600 + 500
= 1200 + 500
= 1700 cm

(b)
Total length of C and B
= 3 u + 750 + 1 u
= 4 u + 750
= 4 x 600 + 750
= 2400 + 750
= 3150 cm

Answer(s): (a) 1700 cm; (b) 3150 cm