A piece of ribbon 2700 cm long is cut into 3 parts, B, A and C.
B is 3 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 = 3 x (1 u + 200) = 3 u + 600
Total length of B, A and C
= 3 u + 600 + 1 u + 200 + 1 u
= 3 u + 1 u + 1 u + 600 + 200
= 5 u + 800
5 u + 800 = 2700
5 u = 2700 - 800
5 u = 1900
1 u = 1900 ÷ 5 = 380
Length of C shorter than B
= 3 u + 600 - 1 u
= 3 u - 1 u + 600
= 2 u + 600
= 2 x 380 + 600
= 760 + 600
= 1360 cm
(b)
Total length of B and A = 3 u + 600 + 1 u + 200
= 3 u + 1 u + 600 + 200
= 4 x 380 + 800 = 1520 + 800 = 2320 cm Answer(s): (a) 1360 cm; (b) 2320 cm