A piece of ribbon 4000 cm long is cut into 3 parts, A, C and B.
A is 4 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 = 4 x (1 u + 200) = 4 u + 800
Total length of A, C and B
= 4 u + 800 + 1 u + 200 + 1 u
= 4 u + 1 u + 1 u + 800 + 200
= 6 u + 1000
6 u + 1000 = 4000
6 u = 4000 - 1000
6 u = 3000
1 u = 3000 ÷ 6 = 500
Length of A longer than C
= 4 u + 800 - (1 u + 200)
= 4 u - 1 u + 800 - 200
= 3 u + 600
= 3 x 500 + 600
= 1500 + 600
= 2100 cm
(b)
Total length of A and B
= 4 u + 800 + 1 u
= 5 u + 800
= 5 x 500 + 800
= 2500 + 800
= 3300 cm
Answer(s): (a) 2100 cm; (b) 3300 cm