A piece of ribbon 2500 cm long is cut into 3 parts, A, C and B.
A is 5 times as long as C.
B is 160 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 + 160
Length of A = 5 x (1 u + 160) = 5 u + 800
Total length of A, C and B
= 5 u + 800 + 1 u + 160 + 1 u
= 5 u + 1 u + 1 u + 800 + 160
= 7 u + 960
7 u + 960 = 2500
7 u = 2500 - 960
7 u = 1540
1 u = 1540 ÷ 7 = 220
Length of B shorter than A
= 5 u + 800 - 1 u
= 5 u - 1 u + 800
= 4 u + 800
= 4 x 220 + 800
= 880 + 800
= 1680 cm
(b)
Total length of A and C = 5 u + 800 + 1 u + 160
= 5 u + 1 u + 800 + 160
= 6 x 220 + 960 = 1320 + 960 = 2280 cm Answer(s): (a) 1680 cm; (b) 2280 cm