A piece of ribbon 2200 cm long is cut into 3 parts, A, B and C.
A is 3 times as long as B.
C is 180 cm shorter than B.
Give the answers in cm.
- How much shorter is C than A?
- What is the total length of A and B?
(a)
Choose the shortest length to be 1 u.
Length of C = 1 u
Length of B = 1 u + 180
Length of A = 3 x (1 u + 180) = 3 u + 540
Total length of A, B and C
= 3 u + 540 + 1 u + 180 + 1 u
= 3 u + 1 u + 1 u + 540 + 180
= 5 u + 720
5 u + 720 = 2200
5 u = 2200 - 720
5 u = 1480
1 u = 1480 ÷ 5 = 296
Length of C shorter than A
= 3 u + 540 - 1 u
= 3 u - 1 u + 540
= 2 u + 540
= 2 x 296 + 540
= 592 + 540
= 1132 cm
(b)
Total length of A and B = 3 u + 540 + 1 u + 180
= 3 u + 1 u + 540 + 180
= 4 x 296 + 720 = 1184 + 720 = 1904 cm Answer(s): (a) 1132 cm; (b) 1904 cm