A piece of ribbon 1200 cm long is cut into 3 parts, A, B and C.
A is 2 times as long as B.
C is 300 cm shorter than B.
Give the answers in cm.
- How much shorter is C than A?
- What is the total length of A and B?
(a)
Choose the shortest length to be 1 u.
Length of C = 1 u
Length of B = 1 u + 300
Length of A = 2 x (1 u + 300) = 2 u + 600
Total length of A, B and C
= 2 u + 600 + 1 u + 300 + 1 u
= 2 u + 1 u + 1 u + 600 + 300
= 4 u + 900
4 u + 900 = 1200
4 u = 1200 - 900
4 u = 300
1 u = 300 ÷ 4 = 75
Length of C shorter than A
= 2 u + 600 - 1 u
= 2 u - 1 u + 600
= 1 u + 600
= 1 x 75 + 600
= 75 + 600
= 675 cm
(b)
Total length of A and B = 2 u + 600 + 1 u + 300
= 2 u + 1 u + 600 + 300
= 3 x 75 + 900 = 225 + 900 = 1125 cm Answer(s): (a) 675 cm; (b) 1125 cm