A piece of ribbon 2200 cm long is cut into 3 parts, B, A and C.
B is 5 times as long as A.
C is 250 cm shorter than A.
Give the answers in cm.
- How much longer is B than A?
- What is the total length of B and C?
(a)
Choose the shortest length to be 1 u.
Length of C = 1 u
Length of A = 1 u + 250
Length of B = 5 x (1 u + 250) = 5 u + 1250
Total length of B, A and C
= 5 u + 1250 + 1 u + 250 + 1 u
= 5 u + 1 u + 1 u + 1250 + 250
= 7 u + 1500
7 u + 1500 = 2200
7 u = 2200 - 1500
7 u = 700
1 u = 700 ÷ 7 = 100
Length of B longer than A
= 5 u + 1250 - (1 u + 250)
= 5 u - 1 u + 1250 - 250
= 4 u + 1000
= 4 x 100 + 1000
= 400 + 1000
= 1400 cm
(b)
Total length of B and C
= 5 u + 1250 + 1 u
= 6 u + 1250
= 6 x 100 + 1250
= 600 + 1250
= 1850 cm
Answer(s): (a) 1400 cm; (b) 1850 cm