A piece of ribbon 2800 cm long is cut into 3 parts, A, B and C.
A is 2 times as long as B.
C is 220 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 + 220
Length of A = 2 x (1 u + 220) = 2 u + 440
Total length of A, B and C
= 2 u + 440 + 1 u + 220 + 1 u
= 2 u + 1 u + 1 u + 440 + 220
= 4 u + 660
4 u + 660 = 2800
4 u = 2800 - 660
4 u = 2140
1 u = 2140 ÷ 4 = 535
Length of A longer than B
= 2 u + 440 - (1 u + 220)
= 2 u - 1 u + 440 - 220
= 1 u + 220
= 1 x 535 + 220
= 535 + 220
= 755 cm
(b)
Total length of A and C
= 2 u + 440 + 1 u
= 3 u + 440
= 3 x 535 + 440
= 1605 + 440
= 2045 cm
Answer(s): (a) 755 cm; (b) 2045 cm