A piece of ribbon 3900 cm long is cut into 3 parts, B, C and A.
B is 5 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 = 5 x (1 u + 300) = 5 u + 1500
Total length of B, C and A
= 5 u + 1500 + 1 u + 300 + 1 u
= 5 u + 1 u + 1 u + 1500 + 300
= 7 u + 1800
7 u + 1800 = 3900
7 u = 3900 - 1800
7 u = 2100
1 u = 2100 ÷ 7 = 300
Length of A shorter than B
= 5 u + 1500 - 1 u
= 5 u - 1 u + 1500
= 4 u + 1500
= 4 x 300 + 1500
= 1200 + 1500
= 2700 cm
(b)
Total length of B and C = 5 u + 1500 + 1 u + 300
= 5 u + 1 u + 1500 + 300
= 6 x 300 + 1800 = 1800 + 1800 = 3600 cm Answer(s): (a) 2700 cm; (b) 3600 cm
