1510.42 – Farmer Fox

Farmer Fox has left his herd of cows to this four daughters. According to the will, the oldest gets half of them, the next youngest gets 1/4, the third gets 1/5 and the youngest gets the remaining 7 cows. How large is the herd?

Solution

Solution. Let xx be the size of the herd. Then

x=x2+x4+x5+7=(12+14+15)x+7=(10+5+4)x20+7=19⋅x20+7 x = \frac{x}{2} + \frac{x}{4} + \frac{x}{5} + 7 =(\frac{1}{2} + \frac{1}{4} + \frac{1}{5})x + 7 = (10 + 5 + 4)\frac{x}{20} + 7 =19\cdot \frac{x}{20} + 7

So x20=7\frac{x}{20} = 7 and x=140x = 140.