A piece of ribbon 3100 cm long is cut into 3 parts, A, B and C.
A is 4 times as long as B.
C is 200 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 + 200
Length of A = 4 x (1 u + 200) = 4 u + 800
Total length of A, B and C
= 4 u + 800 + 1 u + 200 + 1 u
= 4 u + 1 u + 1 u + 800 + 200
= 6 u + 1000
6 u + 1000 = 3100
6 u = 3100 - 1000
6 u = 2100
1 u = 2100 ÷ 6 = 350
Length of A longer than B
= 4 u + 800 - (1 u + 200)
= 4 u - 1 u + 800 - 200
= 3 u + 600
= 3 x 350 + 600
= 1050 + 600
= 1650 cm
(b)
Total length of A and C
= 4 u + 800 + 1 u
= 5 u + 800
= 5 x 350 + 800
= 1750 + 800
= 2550 cm
Answer(s): (a) 1650 cm; (b) 2550 cm