A piece of ribbon 2500 cm long is cut into 3 parts, C, A and B.
C is 3 times as long as A.
B is 120 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 + 120
Length of C = 3 x (1 u + 120) = 3 u + 360
Total length of C, A and B
= 3 u + 360 + 1 u + 120 + 1 u
= 3 u + 1 u + 1 u + 360 + 120
= 5 u + 480
5 u + 480 = 2500
5 u = 2500 - 480
5 u = 2020
1 u = 2020 ÷ 5 = 404
Length of C longer than A
= 3 u + 360 - (1 u + 120)
= 3 u - 1 u + 360 - 120
= 2 u + 240
= 2 x 404 + 240
= 808 + 240
= 1048 cm
(b)
Total length of C and B
= 3 u + 360 + 1 u
= 4 u + 360
= 4 x 404 + 360
= 1616 + 360
= 1976 cm
Answer(s): (a) 1048 cm; (b) 1976 cm