A piece of ribbon 1600 cm long is cut into 3 parts, A, B and C.
A is 3 times as long as B.
C is 240 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 + 240
Length of A = 3 x (1 u + 240) = 3 u + 720
Total length of A, B and C
= 3 u + 720 + 1 u + 240 + 1 u
= 3 u + 1 u + 1 u + 720 + 240
= 5 u + 960
5 u + 960 = 1600
5 u = 1600 - 960
5 u = 640
1 u = 640 ÷ 5 = 128
Length of A longer than B
= 3 u + 720 - (1 u + 240)
= 3 u - 1 u + 720 - 240
= 2 u + 480
= 2 x 128 + 480
= 256 + 480
= 736 cm
(b)
Total length of A and C
= 3 u + 720 + 1 u
= 4 u + 720
= 4 x 128 + 720
= 512 + 720
= 1232 cm
Answer(s): (a) 736 cm; (b) 1232 cm