A piece of ribbon 1100 cm long is cut into 3 parts, A, C and B.
A is 4 times as long as C.
B is 280 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 + 280
Length of A = 4 x (1 u + 280) = 4 u + 1120
Total length of A, C and B
= 4 u + 1120 + 1 u + 280 + 1 u
= 4 u + 1 u + 1 u + 1120 + 280
= 6 u + 1400
6 u + 1400 = 1100
6 u = 1100 - 1400
6 u = -300
1 u = -300 ÷ 6 = -50
Length of A longer than C
= 4 u + 1120 - (1 u + 280)
= 4 u - 1 u + 1120 - 280
= 3 u + 840
= 3 x -50 + 840
= -150 + 840
= 690 cm
(b)
Total length of A and B
= 4 u + 1120 + 1 u
= 5 u + 1120
= 5 x -50 + 1120
= -250 + 1120
= 870 cm
Answer(s): (a) 690 cm; (b) 870 cm