A piece of ribbon 4700 cm long is cut into 3 parts, A, B and C.
A is 3 times as long as B.
C is 230 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 + 230
Length of A = 3 x (1 u + 230) = 3 u + 690
Total length of A, B and C
= 3 u + 690 + 1 u + 230 + 1 u
= 3 u + 1 u + 1 u + 690 + 230
= 5 u + 920
5 u + 920 = 4700
5 u = 4700 - 920
5 u = 3780
1 u = 3780 ÷ 5 = 756
Length of A longer than B
= 3 u + 690 - (1 u + 230)
= 3 u - 1 u + 690 - 230
= 2 u + 460
= 2 x 756 + 460
= 1512 + 460
= 1972 cm
(b)
Total length of A and C
= 3 u + 690 + 1 u
= 4 u + 690
= 4 x 756 + 690
= 3024 + 690
= 3714 cm
Answer(s): (a) 1972 cm; (b) 3714 cm