A piece of ribbon 4300 cm long is cut into 3 parts, C, B and A.
C is 4 times as long as B.
A is 200 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 + 200
Length of C = 4 x (1 u + 200) = 4 u + 800
Total length of C, B and A
= 4 u + 800 + 1 u + 200 + 1 u
= 4 u + 1 u + 1 u + 800 + 200
= 6 u + 1000
6 u + 1000 = 4300
6 u = 4300 - 1000
6 u = 3300
1 u = 3300 ÷ 6 = 550
Length of A shorter than C
= 4 u + 800 - 1 u
= 4 u - 1 u + 800
= 3 u + 800
= 3 x 550 + 800
= 1650 + 800
= 2450 cm
(b)
Total length of C and B = 4 u + 800 + 1 u + 200
= 4 u + 1 u + 800 + 200
= 5 x 550 + 1000 = 2750 + 1000 = 3750 cm Answer(s): (a) 2450 cm; (b) 3750 cm