A piece of ribbon 2400 cm long is cut into 3 parts, A, C and B.
A is 4 times as long as C.
B is 120 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 + 120
Length of A = 4 x (1 u + 120) = 4 u + 480
Total length of A, C and B
= 4 u + 480 + 1 u + 120 + 1 u
= 4 u + 1 u + 1 u + 480 + 120
= 6 u + 600
6 u + 600 = 2400
6 u = 2400 - 600
6 u = 1800
1 u = 1800 ÷ 6 = 300
Length of A longer than C
= 4 u + 480 - (1 u + 120)
= 4 u - 1 u + 480 - 120
= 3 u + 360
= 3 x 300 + 360
= 900 + 360
= 1260 cm
(b)
Total length of A and B
= 4 u + 480 + 1 u
= 5 u + 480
= 5 x 300 + 480
= 1500 + 480
= 1980 cm
Answer(s): (a) 1260 cm; (b) 1980 cm