A piece of ribbon 3900 cm long is cut into 3 parts, A, B and C.
A is 4 times as long as B.
C is 150 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 + 150
Length of A = 4 x (1 u + 150) = 4 u + 600
Total length of A, B and C
= 4 u + 600 + 1 u + 150 + 1 u
= 4 u + 1 u + 1 u + 600 + 150
= 6 u + 750
6 u + 750 = 3900
6 u = 3900 - 750
6 u = 3150
1 u = 3150 ÷ 6 = 525
Length of A longer than B
= 4 u + 600 - (1 u + 150)
= 4 u - 1 u + 600 - 150
= 3 u + 450
= 3 x 525 + 450
= 1575 + 450
= 2025 cm
(b)
Total length of A and C
= 4 u + 600 + 1 u
= 5 u + 600
= 5 x 525 + 600
= 2625 + 600
= 3225 cm
Answer(s): (a) 2025 cm; (b) 3225 cm