A piece of ribbon 4200 cm long is cut into 3 parts, A, B and C.
A is 2 times as long as B.
C is 160 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 + 160
Length of A = 2 x (1 u + 160) = 2 u + 320
Total length of A, B and C
= 2 u + 320 + 1 u + 160 + 1 u
= 2 u + 1 u + 1 u + 320 + 160
= 4 u + 480
4 u + 480 = 4200
4 u = 4200 - 480
4 u = 3720
1 u = 3720 ÷ 4 = 930
Length of A longer than B
= 2 u + 320 - (1 u + 160)
= 2 u - 1 u + 320 - 160
= 1 u + 160
= 1 x 930 + 160
= 930 + 160
= 1090 cm
(b)
Total length of A and C
= 2 u + 320 + 1 u
= 3 u + 320
= 3 x 930 + 320
= 2790 + 320
= 3110 cm
Answer(s): (a) 1090 cm; (b) 3110 cm