A piece of ribbon 4100 cm long is cut into 3 parts, C, B and A.
C is 3 times as long as B.
A is 140 cm shorter than B.
Give the answers in cm.
- How much longer is C than B?
- What is the total length of C and A?
(a)
Choose the shortest length to be 1 u.
Length of A = 1 u
Length of B = 1 u + 140
Length of C = 3 x (1 u + 140) = 3 u + 420
Total length of C, B and A
= 3 u + 420 + 1 u + 140 + 1 u
= 3 u + 1 u + 1 u + 420 + 140
= 5 u + 560
5 u + 560 = 4100
5 u = 4100 - 560
5 u = 3540
1 u = 3540 ÷ 5 = 708
Length of C longer than B
= 3 u + 420 - (1 u + 140)
= 3 u - 1 u + 420 - 140
= 2 u + 280
= 2 x 708 + 280
= 1416 + 280
= 1696 cm
(b)
Total length of C and A
= 3 u + 420 + 1 u
= 4 u + 420
= 4 x 708 + 420
= 2832 + 420
= 3252 cm
Answer(s): (a) 1696 cm; (b) 3252 cm