A piece of ribbon 5000 cm long is cut into 3 parts, C, A and B.
C is 3 times as long as A.
B is 200 cm shorter than A.
Give the answers in cm.
- How much longer is C than A?
- What is the total length of C and B?
(a)
Choose the shortest length to be 1 u.
Length of B = 1 u
Length of A = 1 u + 200
Length of C = 3 x (1 u + 200) = 3 u + 600
Total length of C, A and B
= 3 u + 600 + 1 u + 200 + 1 u
= 3 u + 1 u + 1 u + 600 + 200
= 5 u + 800
5 u + 800 = 5000
5 u = 5000 - 800
5 u = 4200
1 u = 4200 ÷ 5 = 840
Length of C longer than A
= 3 u + 600 - (1 u + 200)
= 3 u - 1 u + 600 - 200
= 2 u + 400
= 2 x 840 + 400
= 1680 + 400
= 2080 cm
(b)
Total length of C and B
= 3 u + 600 + 1 u
= 4 u + 600
= 4 x 840 + 600
= 3360 + 600
= 3960 cm
Answer(s): (a) 2080 cm; (b) 3960 cm