A piece of ribbon 3600 cm long is cut into 3 parts, B, C and A.
B is 4 times as long as C.
A is 300 cm shorter than C.
Give the answers in cm.
- How much shorter is A than B?
- What is the total length of B and C?
(a)
Choose the shortest length to be 1 u.
Length of A = 1 u
Length of C = 1 u + 300
Length of B = 4 x (1 u + 300) = 4 u + 1200
Total length of B, C and A
= 4 u + 1200 + 1 u + 300 + 1 u
= 4 u + 1 u + 1 u + 1200 + 300
= 6 u + 1500
6 u + 1500 = 3600
6 u = 3600 - 1500
6 u = 2100
1 u = 2100 ÷ 6 = 350
Length of A shorter than B
= 4 u + 1200 - 1 u
= 4 u - 1 u + 1200
= 3 u + 1200
= 3 x 350 + 1200
= 1050 + 1200
= 2250 cm
(b)
Total length of B and C = 4 u + 1200 + 1 u + 300
= 4 u + 1 u + 1200 + 300
= 5 x 350 + 1500 = 1750 + 1500 = 3250 cm Answer(s): (a) 2250 cm; (b) 3250 cm