A piece of ribbon 1700 cm long is cut into 3 parts, B, C and A.
B is 2 times as long as C.
A is 120 cm shorter than C.
Give the answers in cm.
- How much longer is B than C?
- What is the total length of B and A?
(a)
Choose the shortest length to be 1 u.
Length of A = 1 u
Length of C = 1 u + 120
Length of B = 2 x (1 u + 120) = 2 u + 240
Total length of B, C and A
= 2 u + 240 + 1 u + 120 + 1 u
= 2 u + 1 u + 1 u + 240 + 120
= 4 u + 360
4 u + 360 = 1700
4 u = 1700 - 360
4 u = 1340
1 u = 1340 ÷ 4 = 335
Length of B longer than C
= 2 u + 240 - (1 u + 120)
= 2 u - 1 u + 240 - 120
= 1 u + 120
= 1 x 335 + 120
= 335 + 120
= 455 cm
(b)
Total length of B and A
= 2 u + 240 + 1 u
= 3 u + 240
= 3 x 335 + 240
= 1005 + 240
= 1245 cm
Answer(s): (a) 455 cm; (b) 1245 cm