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 110 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 + 110
Length of A = 3 x (1 u + 110) = 3 u + 330
Total length of A, C and B
= 3 u + 330 + 1 u + 110 + 1 u
= 3 u + 1 u + 1 u + 330 + 110
= 5 u + 440
5 u + 440 = 1500
5 u = 1500 - 440
5 u = 1060
1 u = 1060 ÷ 5 = 212
Length of A longer than C
= 3 u + 330 - (1 u + 110)
= 3 u - 1 u + 330 - 110
= 2 u + 220
= 2 x 212 + 220
= 424 + 220
= 644 cm
(b)
Total length of A and B
= 3 u + 330 + 1 u
= 4 u + 330
= 4 x 212 + 330
= 848 + 330
= 1178 cm
Answer(s): (a) 644 cm; (b) 1178 cm