A piece of ribbon 2100 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 longer is C than B?
- What is the total length of C and A?
(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 = 2100
5 u = 2100 - 840
5 u = 1260
1 u = 1260 ÷ 5 = 252
Length of C longer than B
= 3 u + 630 - (1 u + 210)
= 3 u - 1 u + 630 - 210
= 2 u + 420
= 2 x 252 + 420
= 504 + 420
= 924 cm
(b)
Total length of C and A
= 3 u + 630 + 1 u
= 4 u + 630
= 4 x 252 + 630
= 1008 + 630
= 1638 cm
Answer(s): (a) 924 cm; (b) 1638 cm