A piece of ribbon 3100 cm long is cut into 3 parts, A, B and C.
A is 2 times as long as B.
C is 200 cm shorter than B.
Give the answers in cm.
- How much shorter is C than A?
- What is the total length of A and B?
(a)
Choose the shortest length to be 1 u.
Length of C = 1 u
Length of B = 1 u + 200
Length of A = 2 x (1 u + 200) = 2 u + 400
Total length of A, B and C
= 2 u + 400 + 1 u + 200 + 1 u
= 2 u + 1 u + 1 u + 400 + 200
= 4 u + 600
4 u + 600 = 3100
4 u = 3100 - 600
4 u = 2500
1 u = 2500 ÷ 4 = 625
Length of C shorter than A
= 2 u + 400 - 1 u
= 2 u - 1 u + 400
= 1 u + 400
= 1 x 625 + 400
= 625 + 400
= 1025 cm
(b)
Total length of A and B = 2 u + 400 + 1 u + 200
= 2 u + 1 u + 400 + 200
= 3 x 625 + 600 = 1875 + 600 = 2475 cm Answer(s): (a) 1025 cm; (b) 2475 cm