A piece of ribbon 5000 cm long is cut into 3 parts, A, B and C.
A is 2 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 = 2 x (1 u + 200) = 2 u + 400
Total length of A, B and C
= 2 u + 400 + 1 u + 200 + 1 u
= 2 u + 1 u + 1 u + 400 + 200
= 4 u + 600
4 u + 600 = 5000
4 u = 5000 - 600
4 u = 4400
1 u = 4400 ÷ 4 = 1100
Length of A longer than B
= 2 u + 400 - (1 u + 200)
= 2 u - 1 u + 400 - 200
= 1 u + 200
= 1 x 1100 + 200
= 1100 + 200
= 1300 cm
(b)
Total length of A and C
= 2 u + 400 + 1 u
= 3 u + 400
= 3 x 1100 + 400
= 3300 + 400
= 3700 cm
Answer(s): (a) 1300 cm; (b) 3700 cm