A piece of ribbon 3900 cm long is cut into 3 parts, C, A and B.
C is 4 times as long as A.
B is 270 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 + 270
Length of C = 4 x (1 u + 270) = 4 u + 1080
Total length of C, A and B
= 4 u + 1080 + 1 u + 270 + 1 u
= 4 u + 1 u + 1 u + 1080 + 270
= 6 u + 1350
6 u + 1350 = 3900
6 u = 3900 - 1350
6 u = 2550
1 u = 2550 ÷ 6 = 425
Length of C longer than A
= 4 u + 1080 - (1 u + 270)
= 4 u - 1 u + 1080 - 270
= 3 u + 810
= 3 x 425 + 810
= 1275 + 810
= 2085 cm
(b)
Total length of C and B
= 4 u + 1080 + 1 u
= 5 u + 1080
= 5 x 425 + 1080
= 2125 + 1080
= 3205 cm
Answer(s): (a) 2085 cm; (b) 3205 cm