A piece of ribbon 2500 cm long is cut into 3 parts, A, C and B.
A is 2 times as long as C.
B is 300 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 + 300
Length of A = 2 x (1 u + 300) = 2 u + 600
Total length of A, C and B
= 2 u + 600 + 1 u + 300 + 1 u
= 2 u + 1 u + 1 u + 600 + 300
= 4 u + 900
4 u + 900 = 2500
4 u = 2500 - 900
4 u = 1600
1 u = 1600 ÷ 4 = 400
Length of A longer than C
= 2 u + 600 - (1 u + 300)
= 2 u - 1 u + 600 - 300
= 1 u + 300
= 1 x 400 + 300
= 400 + 300
= 700 cm
(b)
Total length of A and B
= 2 u + 600 + 1 u
= 3 u + 600
= 3 x 400 + 600
= 1200 + 600
= 1800 cm
Answer(s): (a) 700 cm; (b) 1800 cm