A piece of ribbon 1900 cm long is cut into 3 parts, A, C and B.
A is 2 times as long as C.
B is 220 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 + 220
Length of A = 2 x (1 u + 220) = 2 u + 440
Total length of A, C and B
= 2 u + 440 + 1 u + 220 + 1 u
= 2 u + 1 u + 1 u + 440 + 220
= 4 u + 660
4 u + 660 = 1900
4 u = 1900 - 660
4 u = 1240
1 u = 1240 ÷ 4 = 310
Length of A longer than C
= 2 u + 440 - (1 u + 220)
= 2 u - 1 u + 440 - 220
= 1 u + 220
= 1 x 310 + 220
= 310 + 220
= 530 cm
(b)
Total length of A and B
= 2 u + 440 + 1 u
= 3 u + 440
= 3 x 310 + 440
= 930 + 440
= 1370 cm
Answer(s): (a) 530 cm; (b) 1370 cm