A piece of ribbon 3600 cm long is cut into 3 parts, A, B and C.
A is 2 times as long as B.
C is 180 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 + 180
Length of A = 2 x (1 u + 180) = 2 u + 360
Total length of A, B and C
= 2 u + 360 + 1 u + 180 + 1 u
= 2 u + 1 u + 1 u + 360 + 180
= 4 u + 540
4 u + 540 = 3600
4 u = 3600 - 540
4 u = 3060
1 u = 3060 ÷ 4 = 765
Length of A longer than B
= 2 u + 360 - (1 u + 180)
= 2 u - 1 u + 360 - 180
= 1 u + 180
= 1 x 765 + 180
= 765 + 180
= 945 cm
(b)
Total length of A and C
= 2 u + 360 + 1 u
= 3 u + 360
= 3 x 765 + 360
= 2295 + 360
= 2655 cm
Answer(s): (a) 945 cm; (b) 2655 cm