A piece of ribbon 1200 cm long is cut into 3 parts, C, B and A.
C is 5 times as long as B.
A is 270 cm shorter than B.
Give the answers in cm.
- How much shorter is A than C?
- What is the total length of C and B?
(a)
Choose the shortest length to be 1 u.
Length of A = 1 u
Length of B = 1 u + 270
Length of C = 5 x (1 u + 270) = 5 u + 1350
Total length of C, B and A
= 5 u + 1350 + 1 u + 270 + 1 u
= 5 u + 1 u + 1 u + 1350 + 270
= 7 u + 1620
7 u + 1620 = 1200
7 u = 1200 - 1620
7 u = -420
1 u = -420 ÷ 7 = -60
Length of A shorter than C
= 5 u + 1350 - 1 u
= 5 u - 1 u + 1350
= 4 u + 1350
= 4 x -60 + 1350
= -240 + 1350
= 1110 cm
(b)
Total length of C and B = 5 u + 1350 + 1 u + 270
= 5 u + 1 u + 1350 + 270
= 6 x -60 + 1620 = -360 + 1620 = 1260 cm Answer(s): (a) 1110 cm; (b) 1260 cm
