A piece of ribbon 3000 cm long is cut into 3 parts, B, A and C.
B is 3 times as long as A.
C is 210 cm shorter than A.
Give the answers in cm.
- How much longer is B than A?
- What is the total length of B and C?
(a)
Choose the shortest length to be 1 u.
Length of C = 1 u
Length of A = 1 u + 210
Length of B = 3 x (1 u + 210) = 3 u + 630
Total length of B, A and C
= 3 u + 630 + 1 u + 210 + 1 u
= 3 u + 1 u + 1 u + 630 + 210
= 5 u + 840
5 u + 840 = 3000
5 u = 3000 - 840
5 u = 2160
1 u = 2160 ÷ 5 = 432
Length of B longer than A
= 3 u + 630 - (1 u + 210)
= 3 u - 1 u + 630 - 210
= 2 u + 420
= 2 x 432 + 420
= 864 + 420
= 1284 cm
(b)
Total length of B and C
= 3 u + 630 + 1 u
= 4 u + 630
= 4 x 432 + 630
= 1728 + 630
= 2358 cm
Answer(s): (a) 1284 cm; (b) 2358 cm