A piece of ribbon 2400 cm long is cut into 3 parts, C, B and A.
C is 3 times as long as B.
A is 230 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 + 230
Length of C = 3 x (1 u + 230) = 3 u + 690
Total length of C, B and A
= 3 u + 690 + 1 u + 230 + 1 u
= 3 u + 1 u + 1 u + 690 + 230
= 5 u + 920
5 u + 920 = 2400
5 u = 2400 - 920
5 u = 1480
1 u = 1480 ÷ 5 = 296
Length of A shorter than C
= 3 u + 690 - 1 u
= 3 u - 1 u + 690
= 2 u + 690
= 2 x 296 + 690
= 592 + 690
= 1282 cm
(b)
Total length of C and B = 3 u + 690 + 1 u + 230
= 3 u + 1 u + 690 + 230
= 4 x 296 + 920 = 1184 + 920 = 2104 cm Answer(s): (a) 1282 cm; (b) 2104 cm