A piece of ribbon 2300 cm long is cut into 3 parts, B, C and A.
B is 3 times as long as C.
A is 210 cm shorter than C.
Give the answers in cm.
- How much shorter is A than B?
- What is the total length of B and C?
(a)
Choose the shortest length to be 1 u.
Length of A = 1 u
Length of C = 1 u + 210
Length of B = 3 x (1 u + 210) = 3 u + 630
Total length of B, C and A
= 3 u + 630 + 1 u + 210 + 1 u
= 3 u + 1 u + 1 u + 630 + 210
= 5 u + 840
5 u + 840 = 2300
5 u = 2300 - 840
5 u = 1460
1 u = 1460 ÷ 5 = 292
Length of A shorter than B
= 3 u + 630 - 1 u
= 3 u - 1 u + 630
= 2 u + 630
= 2 x 292 + 630
= 584 + 630
= 1214 cm
(b)
Total length of B and C = 3 u + 630 + 1 u + 210
= 3 u + 1 u + 630 + 210
= 4 x 292 + 840 = 1168 + 840 = 2008 cm Answer(s): (a) 1214 cm; (b) 2008 cm