A piece of ribbon 1200 cm long is cut into 3 parts, C, B and A.
C is 3 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 = 3 x (1 u + 270) = 3 u + 810
Total length of C, B and A
= 3 u + 810 + 1 u + 270 + 1 u
= 3 u + 1 u + 1 u + 810 + 270
= 5 u + 1080
5 u + 1080 = 1200
5 u = 1200 - 1080
5 u = 120
1 u = 120 ÷ 5 = 24
Length of A shorter than C
= 3 u + 810 - 1 u
= 3 u - 1 u + 810
= 2 u + 810
= 2 x 24 + 810
= 48 + 810
= 858 cm
(b)
Total length of C and B = 3 u + 810 + 1 u + 270
= 3 u + 1 u + 810 + 270
= 4 x 24 + 1080 = 96 + 1080 = 1176 cm Answer(s): (a) 858 cm; (b) 1176 cm