There are 240 animals in a farm. 40 goats are added and the fraction av goats is tripled. What is the new amount of goats?
Let the fraction of goats at the start = x/240
Then.....3 times this = 3(x)/240
And when we add 40 to the original number we have that the new fractional amount = (x + 40) / (240 + 40) =
(x + 40) / 280
So we have that
( x + 40)/ 280 = (3x) / 240 cross-multiply
240(x + 40) = 280 (3x) simplify
240x + 9600 = 840x subtract 240x from both sides
9600 = 600x divide both sides by 600
16 = x this is the number of goats at the beginning...and the fractional amount = 16 / 240 = 1/15
At the end....the number of goats = 16 + 40 = 56......and the fractional amount at the end = 56/280 = 1/5
Verify that 3(1/15) indeed = 3/15 = 1/5