A piece of ribbon 4500 cm long is cut into 3 parts, C, B and A.
C is 3 times as long as B.
A is 290 cm shorter than B.
Give the answers in cm.
- How much shorter is A than C?
- What is the total length of C and B?
(a)
Choose the shortest length to be 1 u.
Length of A = 1 u
Length of B = 1 u + 290
Length of C = 3 x (1 u + 290) = 3 u + 870
Total length of C, B and A
= 3 u + 870 + 1 u + 290 + 1 u
= 3 u + 1 u + 1 u + 870 + 290
= 5 u + 1160
5 u + 1160 = 4500
5 u = 4500 - 1160
5 u = 3340
1 u = 3340 ÷ 5 = 668
Length of A shorter than C
= 3 u + 870 - 1 u
= 3 u - 1 u + 870
= 2 u + 870
= 2 x 668 + 870
= 1336 + 870
= 2206 cm
(b)
Total length of C and B = 3 u + 870 + 1 u + 290
= 3 u + 1 u + 870 + 290
= 4 x 668 + 1160 = 2672 + 1160 = 3832 cm Answer(s): (a) 2206 cm; (b) 3832 cm