A piece of ribbon 1600 cm long is cut into 3 parts, C, A and B.
C is 2 times as long as A.
B is 200 cm shorter than A.
Give the answers in cm.
- How much longer is C than A?
- What is the total length of C and B?
(a)
Choose the shortest length to be 1 u.
Length of B = 1 u
Length of A = 1 u + 200
Length of C = 2 x (1 u + 200) = 2 u + 400
Total length of C, A and B
= 2 u + 400 + 1 u + 200 + 1 u
= 2 u + 1 u + 1 u + 400 + 200
= 4 u + 600
4 u + 600 = 1600
4 u = 1600 - 600
4 u = 1000
1 u = 1000 ÷ 4 = 250
Length of C longer than A
= 2 u + 400 - (1 u + 200)
= 2 u - 1 u + 400 - 200
= 1 u + 200
= 1 x 250 + 200
= 250 + 200
= 450 cm
(b)
Total length of C and B
= 2 u + 400 + 1 u
= 3 u + 400
= 3 x 250 + 400
= 750 + 400
= 1150 cm
Answer(s): (a) 450 cm; (b) 1150 cm