A piece of ribbon 2100 cm long is cut into 3 parts, A, B and C.
A is 2 times as long as B.
C is 120 cm shorter than B.
Give the answers in cm.
- How much longer is A than B?
- What is the total length of A and C?
(a)
Choose the shortest length to be 1 u.
Length of C = 1 u
Length of B = 1 u + 120
Length of A = 2 x (1 u + 120) = 2 u + 240
Total length of A, B and C
= 2 u + 240 + 1 u + 120 + 1 u
= 2 u + 1 u + 1 u + 240 + 120
= 4 u + 360
4 u + 360 = 2100
4 u = 2100 - 360
4 u = 1740
1 u = 1740 ÷ 4 = 435
Length of A longer than B
= 2 u + 240 - (1 u + 120)
= 2 u - 1 u + 240 - 120
= 1 u + 120
= 1 x 435 + 120
= 435 + 120
= 555 cm
(b)
Total length of A and C
= 2 u + 240 + 1 u
= 3 u + 240
= 3 x 435 + 240
= 1305 + 240
= 1545 cm
Answer(s): (a) 555 cm; (b) 1545 cm