A piece of ribbon 3400 cm long is cut into 3 parts, A, C and B.
A is 3 times as long as C.
B is 150 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 + 150
Length of A = 3 x (1 u + 150) = 3 u + 450
Total length of A, C and B
= 3 u + 450 + 1 u + 150 + 1 u
= 3 u + 1 u + 1 u + 450 + 150
= 5 u + 600
5 u + 600 = 3400
5 u = 3400 - 600
5 u = 2800
1 u = 2800 ÷ 5 = 560
Length of B shorter than A
= 3 u + 450 - 1 u
= 3 u - 1 u + 450
= 2 u + 450
= 2 x 560 + 450
= 1120 + 450
= 1570 cm
(b)
Total length of A and C = 3 u + 450 + 1 u + 150
= 3 u + 1 u + 450 + 150
= 4 x 560 + 600 = 2240 + 600 = 2840 cm Answer(s): (a) 1570 cm; (b) 2840 cm