A piece of ribbon 3400 cm long is cut into 3 parts, C, B and A.
C is 2 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 = 2 x (1 u + 200) = 2 u + 400
Total length of C, B and A
= 2 u + 400 + 1 u + 200 + 1 u
= 2 u + 1 u + 1 u + 400 + 200
= 4 u + 600
4 u + 600 = 3400
4 u = 3400 - 600
4 u = 2800
1 u = 2800 ÷ 4 = 700
Length of A shorter than C
= 2 u + 400 - 1 u
= 2 u - 1 u + 400
= 1 u + 400
= 1 x 700 + 400
= 700 + 400
= 1100 cm
(b)
Total length of C and B = 2 u + 400 + 1 u + 200
= 2 u + 1 u + 400 + 200
= 3 x 700 + 600 = 2100 + 600 = 2700 cm Answer(s): (a) 1100 cm; (b) 2700 cm