A piece of ribbon 3500 cm long is cut into 3 parts, C, A and B.
C is 5 times as long as A.
B is 210 cm shorter than A.
Give the answers in cm.
- How much shorter is B than C?
- What is the total length of C and A?
(a)
Choose the shortest length to be 1 u.
Length of B = 1 u
Length of A = 1 u + 210
Length of C = 5 x (1 u + 210) = 5 u + 1050
Total length of C, A and B
= 5 u + 1050 + 1 u + 210 + 1 u
= 5 u + 1 u + 1 u + 1050 + 210
= 7 u + 1260
7 u + 1260 = 3500
7 u = 3500 - 1260
7 u = 2240
1 u = 2240 ÷ 7 = 320
Length of B shorter than C
= 5 u + 1050 - 1 u
= 5 u - 1 u + 1050
= 4 u + 1050
= 4 x 320 + 1050
= 1280 + 1050
= 2330 cm
(b)
Total length of C and A = 5 u + 1050 + 1 u + 210
= 5 u + 1 u + 1050 + 210
= 6 x 320 + 1260 = 1920 + 1260 = 3180 cm Answer(s): (a) 2330 cm; (b) 3180 cm