A piece of ribbon 2800 cm long is cut into 3 parts, A, B and C.
A is 5 times as long as B.
C is 280 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 + 280
Length of A = 5 x (1 u + 280) = 5 u + 1400
Total length of A, B and C
= 5 u + 1400 + 1 u + 280 + 1 u
= 5 u + 1 u + 1 u + 1400 + 280
= 7 u + 1680
7 u + 1680 = 2800
7 u = 2800 - 1680
7 u = 1120
1 u = 1120 ÷ 7 = 160
Length of C shorter than A
= 5 u + 1400 - 1 u
= 5 u - 1 u + 1400
= 4 u + 1400
= 4 x 160 + 1400
= 640 + 1400
= 2040 cm
(b)
Total length of A and B = 5 u + 1400 + 1 u + 280
= 5 u + 1 u + 1400 + 280
= 6 x 160 + 1680 = 960 + 1680 = 2640 cm Answer(s): (a) 2040 cm; (b) 2640 cm