A piece of ribbon 4700 cm long is cut into 3 parts, C, B and A.
C is 5 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 = 5 x (1 u + 200) = 5 u + 1000
Total length of C, B and A
= 5 u + 1000 + 1 u + 200 + 1 u
= 5 u + 1 u + 1 u + 1000 + 200
= 7 u + 1200
7 u + 1200 = 4700
7 u = 4700 - 1200
7 u = 3500
1 u = 3500 ÷ 7 = 500
Length of A shorter than C
= 5 u + 1000 - 1 u
= 5 u - 1 u + 1000
= 4 u + 1000
= 4 x 500 + 1000
= 2000 + 1000
= 3000 cm
(b)
Total length of C and B = 5 u + 1000 + 1 u + 200
= 5 u + 1 u + 1000 + 200
= 6 x 500 + 1200 = 3000 + 1200 = 4200 cm Answer(s): (a) 3000 cm; (b) 4200 cm