A piece of ribbon 3800 cm long is cut into 3 parts, A, C and B.
A is 2 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 = 2 x (1 u + 200) = 2 u + 400
Total length of A, C and B
= 2 u + 400 + 1 u + 200 + 1 u
= 2 u + 1 u + 1 u + 400 + 200
= 4 u + 600
4 u + 600 = 3800
4 u = 3800 - 600
4 u = 3200
1 u = 3200 ÷ 4 = 800
Length of A longer than C
= 2 u + 400 - (1 u + 200)
= 2 u - 1 u + 400 - 200
= 1 u + 200
= 1 x 800 + 200
= 800 + 200
= 1000 cm
(b)
Total length of A and B
= 2 u + 400 + 1 u
= 3 u + 400
= 3 x 800 + 400
= 2400 + 400
= 2800 cm
Answer(s): (a) 1000 cm; (b) 2800 cm