A piece of ribbon 1100 cm long is cut into 3 parts, A, B and C.
A is 2 times as long as B.
C is 220 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 + 220
Length of A = 2 x (1 u + 220) = 2 u + 440
Total length of A, B and C
= 2 u + 440 + 1 u + 220 + 1 u
= 2 u + 1 u + 1 u + 440 + 220
= 4 u + 660
4 u + 660 = 1100
4 u = 1100 - 660
4 u = 440
1 u = 440 ÷ 4 = 110
Length of C shorter than A
= 2 u + 440 - 1 u
= 2 u - 1 u + 440
= 1 u + 440
= 1 x 110 + 440
= 110 + 440
= 550 cm
(b)
Total length of A and B = 2 u + 440 + 1 u + 220
= 2 u + 1 u + 440 + 220
= 3 x 110 + 660 = 330 + 660 = 990 cm Answer(s): (a) 550 cm; (b) 990 cm