A piece of ribbon 1100 cm long is cut into 3 parts, B, A and C.
B is 2 times as long as A.
C is 200 cm shorter than A.
Give the answers in cm.
- How much shorter is C than B?
- What is the total length of B and A?
(a)
Choose the shortest length to be 1 u.
Length of C = 1 u
Length of A = 1 u + 200
Length of B = 2 x (1 u + 200) = 2 u + 400
Total length of B, A and C
= 2 u + 400 + 1 u + 200 + 1 u
= 2 u + 1 u + 1 u + 400 + 200
= 4 u + 600
4 u + 600 = 1100
4 u = 1100 - 600
4 u = 500
1 u = 500 ÷ 4 = 125
Length of C shorter than B
= 2 u + 400 - 1 u
= 2 u - 1 u + 400
= 1 u + 400
= 1 x 125 + 400
= 125 + 400
= 525 cm
(b)
Total length of B and A = 2 u + 400 + 1 u + 200
= 2 u + 1 u + 400 + 200
= 3 x 125 + 600 = 375 + 600 = 975 cm Answer(s): (a) 525 cm; (b) 975 cm