A piece of ribbon 3600 cm long is cut into 3 parts, C, A and B.
C is 3 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 = 3 x (1 u + 270) = 3 u + 810
Total length of C, A and B
= 3 u + 810 + 1 u + 270 + 1 u
= 3 u + 1 u + 1 u + 810 + 270
= 5 u + 1080
5 u + 1080 = 3600
5 u = 3600 - 1080
5 u = 2520
1 u = 2520 ÷ 5 = 504
Length of C longer than A
= 3 u + 810 - (1 u + 270)
= 3 u - 1 u + 810 - 270
= 2 u + 540
= 2 x 504 + 540
= 1008 + 540
= 1548 cm
(b)
Total length of C and B
= 3 u + 810 + 1 u
= 4 u + 810
= 4 x 504 + 810
= 2016 + 810
= 2826 cm
Answer(s): (a) 1548 cm; (b) 2826 cm