A piece of ribbon 2400 cm long is cut into 3 parts, C, B and A.
C is 3 times as long as B.
A is 300 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 + 300
Length of C = 3 x (1 u + 300) = 3 u + 900
Total length of C, B and A
= 3 u + 900 + 1 u + 300 + 1 u
= 3 u + 1 u + 1 u + 900 + 300
= 5 u + 1200
5 u + 1200 = 2400
5 u = 2400 - 1200
5 u = 1200
1 u = 1200 ÷ 5 = 240
Length of A shorter than C
= 3 u + 900 - 1 u
= 3 u - 1 u + 900
= 2 u + 900
= 2 x 240 + 900
= 480 + 900
= 1380 cm
(b)
Total length of C and B = 3 u + 900 + 1 u + 300
= 3 u + 1 u + 900 + 300
= 4 x 240 + 1200 = 960 + 1200 = 2160 cm Answer(s): (a) 1380 cm; (b) 2160 cm