A piece of ribbon 3000 cm long is cut into 3 parts, B, C and A.
B is 3 times as long as C.
A is 110 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 + 110
Length of B = 3 x (1 u + 110) = 3 u + 330
Total length of B, C and A
= 3 u + 330 + 1 u + 110 + 1 u
= 3 u + 1 u + 1 u + 330 + 110
= 5 u + 440
5 u + 440 = 3000
5 u = 3000 - 440
5 u = 2560
1 u = 2560 ÷ 5 = 512
Length of A shorter than B
= 3 u + 330 - 1 u
= 3 u - 1 u + 330
= 2 u + 330
= 2 x 512 + 330
= 1024 + 330
= 1354 cm
(b)
Total length of B and C = 3 u + 330 + 1 u + 110
= 3 u + 1 u + 330 + 110
= 4 x 512 + 440 = 2048 + 440 = 2488 cm Answer(s): (a) 1354 cm; (b) 2488 cm