A piece of ribbon 2800 cm long is cut into 3 parts, C, B and A.
C is 3 times as long as B.
A is 180 cm shorter than B.
Give the answers in cm.
- How much shorter is A than C?
- What is the total length of C and B?
(a)
Choose the shortest length to be 1 u.
Length of A = 1 u
Length of B = 1 u + 180
Length of C = 3 x (1 u + 180) = 3 u + 540
Total length of C, B and A
= 3 u + 540 + 1 u + 180 + 1 u
= 3 u + 1 u + 1 u + 540 + 180
= 5 u + 720
5 u + 720 = 2800
5 u = 2800 - 720
5 u = 2080
1 u = 2080 ÷ 5 = 416
Length of A shorter than C
= 3 u + 540 - 1 u
= 3 u - 1 u + 540
= 2 u + 540
= 2 x 416 + 540
= 832 + 540
= 1372 cm
(b)
Total length of C and B = 3 u + 540 + 1 u + 180
= 3 u + 1 u + 540 + 180
= 4 x 416 + 720 = 1664 + 720 = 2384 cm Answer(s): (a) 1372 cm; (b) 2384 cm