A piece of ribbon 4700 cm long is cut into 3 parts, C, A and B.
C is 4 times as long as A.
B is 280 cm shorter than A.
Give the answers in cm.
- How much longer is C than A?
- What is the total length of C and B?
(a)
Choose the shortest length to be 1 u.
Length of B = 1 u
Length of A = 1 u + 280
Length of C = 4 x (1 u + 280) = 4 u + 1120
Total length of C, A and B
= 4 u + 1120 + 1 u + 280 + 1 u
= 4 u + 1 u + 1 u + 1120 + 280
= 6 u + 1400
6 u + 1400 = 4700
6 u = 4700 - 1400
6 u = 3300
1 u = 3300 ÷ 6 = 550
Length of C longer than A
= 4 u + 1120 - (1 u + 280)
= 4 u - 1 u + 1120 - 280
= 3 u + 840
= 3 x 550 + 840
= 1650 + 840
= 2490 cm
(b)
Total length of C and B
= 4 u + 1120 + 1 u
= 5 u + 1120
= 5 x 550 + 1120
= 2750 + 1120
= 3870 cm
Answer(s): (a) 2490 cm; (b) 3870 cm