A piece of ribbon 3600 cm long is cut into 3 parts, A, B and C.
A is 2 times as long as B.
C is 300 cm shorter than B.
Give the answers in cm.
- How much longer is A than B?
- What is the total length of A and C?
(a)
Choose the shortest length to be 1 u.
Length of C = 1 u
Length of B = 1 u + 300
Length of A = 2 x (1 u + 300) = 2 u + 600
Total length of A, B and C
= 2 u + 600 + 1 u + 300 + 1 u
= 2 u + 1 u + 1 u + 600 + 300
= 4 u + 900
4 u + 900 = 3600
4 u = 3600 - 900
4 u = 2700
1 u = 2700 ÷ 4 = 675
Length of A longer than B
= 2 u + 600 - (1 u + 300)
= 2 u - 1 u + 600 - 300
= 1 u + 300
= 1 x 675 + 300
= 675 + 300
= 975 cm
(b)
Total length of A and C
= 2 u + 600 + 1 u
= 3 u + 600
= 3 x 675 + 600
= 2025 + 600
= 2625 cm
Answer(s): (a) 975 cm; (b) 2625 cm