A piece of ribbon 1500 cm long is cut into 3 parts, A, B and C.
A is 3 times as long as B.
C is 200 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 + 200
Length of A = 3 x (1 u + 200) = 3 u + 600
Total length of A, B and C
= 3 u + 600 + 1 u + 200 + 1 u
= 3 u + 1 u + 1 u + 600 + 200
= 5 u + 800
5 u + 800 = 1500
5 u = 1500 - 800
5 u = 700
1 u = 700 ÷ 5 = 140
Length of C shorter than A
= 3 u + 600 - 1 u
= 3 u - 1 u + 600
= 2 u + 600
= 2 x 140 + 600
= 280 + 600
= 880 cm
(b)
Total length of A and B = 3 u + 600 + 1 u + 200
= 3 u + 1 u + 600 + 200
= 4 x 140 + 800 = 560 + 800 = 1360 cm Answer(s): (a) 880 cm; (b) 1360 cm