A piece of ribbon 3000 cm long is cut into 3 parts, B, A and C.
B is 4 times as long as A.
C is 180 cm shorter than A.
Give the answers in cm.
- How much longer is B than A?
- What is the total length of B and C?
(a)
Choose the shortest length to be 1 u.
Length of C = 1 u
Length of A = 1 u + 180
Length of B = 4 x (1 u + 180) = 4 u + 720
Total length of B, A and C
= 4 u + 720 + 1 u + 180 + 1 u
= 4 u + 1 u + 1 u + 720 + 180
= 6 u + 900
6 u + 900 = 3000
6 u = 3000 - 900
6 u = 2100
1 u = 2100 ÷ 6 = 350
Length of B longer than A
= 4 u + 720 - (1 u + 180)
= 4 u - 1 u + 720 - 180
= 3 u + 540
= 3 x 350 + 540
= 1050 + 540
= 1590 cm
(b)
Total length of B and C
= 4 u + 720 + 1 u
= 5 u + 720
= 5 x 350 + 720
= 1750 + 720
= 2470 cm
Answer(s): (a) 1590 cm; (b) 2470 cm