A piece of ribbon 2200 cm long is cut into 3 parts, A, C and B.
A is 3 times as long as C.
B is 200 cm shorter than C.
Give the answers in cm.
- How much longer is A than C?
- What is the total length of A and B?
(a)
Choose the shortest length to be 1 u.
Length of B = 1 u
Length of C = 1 u + 200
Length of A = 3 x (1 u + 200) = 3 u + 600
Total length of A, C and B
= 3 u + 600 + 1 u + 200 + 1 u
= 3 u + 1 u + 1 u + 600 + 200
= 5 u + 800
5 u + 800 = 2200
5 u = 2200 - 800
5 u = 1400
1 u = 1400 ÷ 5 = 280
Length of A longer than C
= 3 u + 600 - (1 u + 200)
= 3 u - 1 u + 600 - 200
= 2 u + 400
= 2 x 280 + 400
= 560 + 400
= 960 cm
(b)
Total length of A and B
= 3 u + 600 + 1 u
= 4 u + 600
= 4 x 280 + 600
= 1120 + 600
= 1720 cm
Answer(s): (a) 960 cm; (b) 1720 cm