A piece of ribbon 3000 cm long is cut into 3 parts, C, B and A.
C is 3 times as long as B.
A is 210 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 + 210
Length of C = 3 x (1 u + 210) = 3 u + 630
Total length of C, B and A
= 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 A shorter than C
= 3 u + 630 - 1 u
= 3 u - 1 u + 630
= 2 u + 630
= 2 x 432 + 630
= 864 + 630
= 1494 cm
(b)
Total length of C and B = 3 u + 630 + 1 u + 210
= 3 u + 1 u + 630 + 210
= 4 x 432 + 840 = 1728 + 840 = 2568 cm Answer(s): (a) 1494 cm; (b) 2568 cm