A piece of ribbon 3100 cm long is cut into 3 parts, B, C and A.
B is 2 times as long as C.
A is 300 cm shorter than C.
Give the answers in cm.
- How much shorter is A than B?
- What is the total length of B and C?
(a)
Choose the shortest length to be 1 u.
Length of A = 1 u
Length of C = 1 u + 300
Length of B = 2 x (1 u + 300) = 2 u + 600
Total length of B, C and A
= 2 u + 600 + 1 u + 300 + 1 u
= 2 u + 1 u + 1 u + 600 + 300
= 4 u + 900
4 u + 900 = 3100
4 u = 3100 - 900
4 u = 2200
1 u = 2200 ÷ 4 = 550
Length of A shorter than B
= 2 u + 600 - 1 u
= 2 u - 1 u + 600
= 1 u + 600
= 1 x 550 + 600
= 550 + 600
= 1150 cm
(b)
Total length of B and C = 2 u + 600 + 1 u + 300
= 2 u + 1 u + 600 + 300
= 3 x 550 + 900 = 1650 + 900 = 2550 cm Answer(s): (a) 1150 cm; (b) 2550 cm