A piece of ribbon 2900 cm long is cut into 3 parts, A, B and C.
A is 3 times as long as B.
C is 150 cm shorter than B.
Give the answers in cm.
- How much longer is A than B?
- What is the total length of A and C?
(a)
Choose the shortest length to be 1 u.
Length of C = 1 u
Length of B = 1 u + 150
Length of A = 3 x (1 u + 150) = 3 u + 450
Total length of A, B and C
= 3 u + 450 + 1 u + 150 + 1 u
= 3 u + 1 u + 1 u + 450 + 150
= 5 u + 600
5 u + 600 = 2900
5 u = 2900 - 600
5 u = 2300
1 u = 2300 ÷ 5 = 460
Length of A longer than B
= 3 u + 450 - (1 u + 150)
= 3 u - 1 u + 450 - 150
= 2 u + 300
= 2 x 460 + 300
= 920 + 300
= 1220 cm
(b)
Total length of A and C
= 3 u + 450 + 1 u
= 4 u + 450
= 4 x 460 + 450
= 1840 + 450
= 2290 cm
Answer(s): (a) 1220 cm; (b) 2290 cm