A piece of ribbon 2200 cm long is cut into 3 parts, C, A and B.
C is 4 times as long as A.
B is 200 cm shorter than A.
Give the answers in cm.
- How much longer is C than A?
- What is the total length of C and B?
(a)
Choose the shortest length to be 1 u.
Length of B = 1 u
Length of A = 1 u + 200
Length of C = 4 x (1 u + 200) = 4 u + 800
Total length of C, A and B
= 4 u + 800 + 1 u + 200 + 1 u
= 4 u + 1 u + 1 u + 800 + 200
= 6 u + 1000
6 u + 1000 = 2200
6 u = 2200 - 1000
6 u = 1200
1 u = 1200 ÷ 6 = 200
Length of C longer than A
= 4 u + 800 - (1 u + 200)
= 4 u - 1 u + 800 - 200
= 3 u + 600
= 3 x 200 + 600
= 600 + 600
= 1200 cm
(b)
Total length of C and B
= 4 u + 800 + 1 u
= 5 u + 800
= 5 x 200 + 800
= 1000 + 800
= 1800 cm
Answer(s): (a) 1200 cm; (b) 1800 cm