A piece of ribbon 5000 cm long is cut into 3 parts, A, B and C.
A is 2 times as long as B.
C is 180 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 + 180
Length of A = 2 x (1 u + 180) = 2 u + 360
Total length of A, B and C
= 2 u + 360 + 1 u + 180 + 1 u
= 2 u + 1 u + 1 u + 360 + 180
= 4 u + 540
4 u + 540 = 5000
4 u = 5000 - 540
4 u = 4460
1 u = 4460 ÷ 4 = 1115
Length of C shorter than A
= 2 u + 360 - 1 u
= 2 u - 1 u + 360
= 1 u + 360
= 1 x 1115 + 360
= 1115 + 360
= 1475 cm
(b)
Total length of A and B = 2 u + 360 + 1 u + 180
= 2 u + 1 u + 360 + 180
= 3 x 1115 + 540 = 3345 + 540 = 3885 cm Answer(s): (a) 1475 cm; (b) 3885 cm