A piece of ribbon 2400 cm long is cut into 3 parts, A, C and B.
A is 3 times as long as C.
B is 250 cm shorter than C.
Give the answers in cm.
- How much longer is A than C?
- What is the total length of A and B?
(a)
Choose the shortest length to be 1 u.
Length of B = 1 u
Length of C = 1 u + 250
Length of A = 3 x (1 u + 250) = 3 u + 750
Total length of A, C and B
= 3 u + 750 + 1 u + 250 + 1 u
= 3 u + 1 u + 1 u + 750 + 250
= 5 u + 1000
5 u + 1000 = 2400
5 u = 2400 - 1000
5 u = 1400
1 u = 1400 ÷ 5 = 280
Length of A longer than C
= 3 u + 750 - (1 u + 250)
= 3 u - 1 u + 750 - 250
= 2 u + 500
= 2 x 280 + 500
= 560 + 500
= 1060 cm
(b)
Total length of A and B
= 3 u + 750 + 1 u
= 4 u + 750
= 4 x 280 + 750
= 1120 + 750
= 1870 cm
Answer(s): (a) 1060 cm; (b) 1870 cm