A piece of ribbon 4900 cm long is cut into 3 parts, A, C and B.
A is 3 times as long as C.
B is 140 cm shorter than C.
Give the answers in cm.
- How much shorter is B than A?
- What is the total length of A and C?
(a)
Choose the shortest length to be 1 u.
Length of B = 1 u
Length of C = 1 u + 140
Length of A = 3 x (1 u + 140) = 3 u + 420
Total length of A, C and B
= 3 u + 420 + 1 u + 140 + 1 u
= 3 u + 1 u + 1 u + 420 + 140
= 5 u + 560
5 u + 560 = 4900
5 u = 4900 - 560
5 u = 4340
1 u = 4340 ÷ 5 = 868
Length of B shorter than A
= 3 u + 420 - 1 u
= 3 u - 1 u + 420
= 2 u + 420
= 2 x 868 + 420
= 1736 + 420
= 2156 cm
(b)
Total length of A and C = 3 u + 420 + 1 u + 140
= 3 u + 1 u + 420 + 140
= 4 x 868 + 560 = 3472 + 560 = 4032 cm Answer(s): (a) 2156 cm; (b) 4032 cm