A piece of ribbon 4200 cm long is cut into 3 parts, B, C and A.
B is 3 times as long as C.
A is 230 cm shorter than C.
Give the answers in cm.
- How much shorter is A than B?
- What is the total length of B and C?
(a)
Choose the shortest length to be 1 u.
Length of A = 1 u
Length of C = 1 u + 230
Length of B = 3 x (1 u + 230) = 3 u + 690
Total length of B, C and A
= 3 u + 690 + 1 u + 230 + 1 u
= 3 u + 1 u + 1 u + 690 + 230
= 5 u + 920
5 u + 920 = 4200
5 u = 4200 - 920
5 u = 3280
1 u = 3280 ÷ 5 = 656
Length of A shorter than B
= 3 u + 690 - 1 u
= 3 u - 1 u + 690
= 2 u + 690
= 2 x 656 + 690
= 1312 + 690
= 2002 cm
(b)
Total length of B and C = 3 u + 690 + 1 u + 230
= 3 u + 1 u + 690 + 230
= 4 x 656 + 920 = 2624 + 920 = 3544 cm Answer(s): (a) 2002 cm; (b) 3544 cm