A piece of ribbon 3200 cm long is cut into 3 parts, A, C and B.
A is 3 times as long as C.
B is 240 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 + 240
Length of A = 3 x (1 u + 240) = 3 u + 720
Total length of A, C and B
= 3 u + 720 + 1 u + 240 + 1 u
= 3 u + 1 u + 1 u + 720 + 240
= 5 u + 960
5 u + 960 = 3200
5 u = 3200 - 960
5 u = 2240
1 u = 2240 ÷ 5 = 448
Length of B shorter than A
= 3 u + 720 - 1 u
= 3 u - 1 u + 720
= 2 u + 720
= 2 x 448 + 720
= 896 + 720
= 1616 cm
(b)
Total length of A and C = 3 u + 720 + 1 u + 240
= 3 u + 1 u + 720 + 240
= 4 x 448 + 960 = 1792 + 960 = 2752 cm Answer(s): (a) 1616 cm; (b) 2752 cm