A piece of ribbon 4000 cm long is cut into 3 parts, A, B and C.
A is 3 times as long as B.
C is 210 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 + 210
Length of A = 3 x (1 u + 210) = 3 u + 630
Total length of A, B and C
= 3 u + 630 + 1 u + 210 + 1 u
= 3 u + 1 u + 1 u + 630 + 210
= 5 u + 840
5 u + 840 = 4000
5 u = 4000 - 840
5 u = 3160
1 u = 3160 ÷ 5 = 632
Length of A longer than B
= 3 u + 630 - (1 u + 210)
= 3 u - 1 u + 630 - 210
= 2 u + 420
= 2 x 632 + 420
= 1264 + 420
= 1684 cm
(b)
Total length of A and C
= 3 u + 630 + 1 u
= 4 u + 630
= 4 x 632 + 630
= 2528 + 630
= 3158 cm
Answer(s): (a) 1684 cm; (b) 3158 cm