A piece of ribbon 5000 cm long is cut into 3 parts, B, A and C.
B is 3 times as long as A.
C is 280 cm shorter than A.
Give the answers in cm.
- How much shorter is C than B?
- What is the total length of B and A?
(a)
Choose the shortest length to be 1 u.
Length of C = 1 u
Length of A = 1 u + 280
Length of B = 3 x (1 u + 280) = 3 u + 840
Total length of B, A and C
= 3 u + 840 + 1 u + 280 + 1 u
= 3 u + 1 u + 1 u + 840 + 280
= 5 u + 1120
5 u + 1120 = 5000
5 u = 5000 - 1120
5 u = 3880
1 u = 3880 ÷ 5 = 776
Length of C shorter than B
= 3 u + 840 - 1 u
= 3 u - 1 u + 840
= 2 u + 840
= 2 x 776 + 840
= 1552 + 840
= 2392 cm
(b)
Total length of B and A = 3 u + 840 + 1 u + 280
= 3 u + 1 u + 840 + 280
= 4 x 776 + 1120 = 3104 + 1120 = 4224 cm Answer(s): (a) 2392 cm; (b) 4224 cm