A piece of ribbon 1800 cm long is cut into 3 parts, C, A and B.
C is 5 times as long as A.
B is 230 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 + 230
Length of C = 5 x (1 u + 230) = 5 u + 1150
Total length of C, A and B
= 5 u + 1150 + 1 u + 230 + 1 u
= 5 u + 1 u + 1 u + 1150 + 230
= 7 u + 1380
7 u + 1380 = 1800
7 u = 1800 - 1380
7 u = 420
1 u = 420 ÷ 7 = 60
Length of C longer than A
= 5 u + 1150 - (1 u + 230)
= 5 u - 1 u + 1150 - 230
= 4 u + 920
= 4 x 60 + 920
= 240 + 920
= 1160 cm
(b)
Total length of C and B
= 5 u + 1150 + 1 u
= 6 u + 1150
= 6 x 60 + 1150
= 360 + 1150
= 1510 cm
Answer(s): (a) 1160 cm; (b) 1510 cm