A piece of ribbon 2200 cm long is cut into 3 parts, C, B and A.
C is 2 times as long as B.
A is 180 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 + 180
Length of C = 2 x (1 u + 180) = 2 u + 360
Total length of C, B and A
= 2 u + 360 + 1 u + 180 + 1 u
= 2 u + 1 u + 1 u + 360 + 180
= 4 u + 540
4 u + 540 = 2200
4 u = 2200 - 540
4 u = 1660
1 u = 1660 ÷ 4 = 415
Length of A shorter than C
= 2 u + 360 - 1 u
= 2 u - 1 u + 360
= 1 u + 360
= 1 x 415 + 360
= 415 + 360
= 775 cm
(b)
Total length of C and B = 2 u + 360 + 1 u + 180
= 2 u + 1 u + 360 + 180
= 3 x 415 + 540 = 1245 + 540 = 1785 cm Answer(s): (a) 775 cm; (b) 1785 cm