A piece of ribbon 1500 cm long is cut into 3 parts, A, C and B.
A is 3 times as long as C.
B is 230 cm shorter than C.
Give the answers in cm.
- How much longer is A than C?
- What is the total length of A and B?
(a)
Choose the shortest length to be 1 u.
Length of B = 1 u
Length of C = 1 u + 230
Length of A = 3 x (1 u + 230) = 3 u + 690
Total length of A, C and B
= 3 u + 690 + 1 u + 230 + 1 u
= 3 u + 1 u + 1 u + 690 + 230
= 5 u + 920
5 u + 920 = 1500
5 u = 1500 - 920
5 u = 580
1 u = 580 ÷ 5 = 116
Length of A longer than C
= 3 u + 690 - (1 u + 230)
= 3 u - 1 u + 690 - 230
= 2 u + 460
= 2 x 116 + 460
= 232 + 460
= 692 cm
(b)
Total length of A and B
= 3 u + 690 + 1 u
= 4 u + 690
= 4 x 116 + 690
= 464 + 690
= 1154 cm
Answer(s): (a) 692 cm; (b) 1154 cm