A piece of ribbon 5000 cm long is cut into 3 parts, C, A and B.
C is 3 times as long as A.
B is 170 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 + 170
Length of C = 3 x (1 u + 170) = 3 u + 510
Total length of C, A and B
= 3 u + 510 + 1 u + 170 + 1 u
= 3 u + 1 u + 1 u + 510 + 170
= 5 u + 680
5 u + 680 = 5000
5 u = 5000 - 680
5 u = 4320
1 u = 4320 ÷ 5 = 864
Length of C longer than A
= 3 u + 510 - (1 u + 170)
= 3 u - 1 u + 510 - 170
= 2 u + 340
= 2 x 864 + 340
= 1728 + 340
= 2068 cm
(b)
Total length of C and B
= 3 u + 510 + 1 u
= 4 u + 510
= 4 x 864 + 510
= 3456 + 510
= 3966 cm
Answer(s): (a) 2068 cm; (b) 3966 cm