A piece of ribbon 1200 cm long is cut into 3 parts, B, C and A.
B is 2 times as long as C.
A is 200 cm shorter than C.
Give the answers in cm.
- How much longer is B than C?
- What is the total length of B and A?
(a)
Choose the shortest length to be 1 u.
Length of A = 1 u
Length of C = 1 u + 200
Length of B = 2 x (1 u + 200) = 2 u + 400
Total length of B, C and A
= 2 u + 400 + 1 u + 200 + 1 u
= 2 u + 1 u + 1 u + 400 + 200
= 4 u + 600
4 u + 600 = 1200
4 u = 1200 - 600
4 u = 600
1 u = 600 ÷ 4 = 150
Length of B longer than C
= 2 u + 400 - (1 u + 200)
= 2 u - 1 u + 400 - 200
= 1 u + 200
= 1 x 150 + 200
= 150 + 200
= 350 cm
(b)
Total length of B and A
= 2 u + 400 + 1 u
= 3 u + 400
= 3 x 150 + 400
= 450 + 400
= 850 cm
Answer(s): (a) 350 cm; (b) 850 cm