Meadow

On the meadow, there are horses, cows, and sheep grazing together with less than 200. If cows were 45 times more, horses 60 times more, and sheep 35 times more than there are now, their numbers would equal. How many
horses, cows, and sheep are in the meadow together?

Correct answer:

x₁ =  85
x₂ =  170

Step-by-step explanation:

$$\begin{gathered} x=a+b+c<200 \\ b=45/60a \\ c=45/35a \\ a+45/60a+45/35a<200 \\ 1...\text{ prime number} \\ 60=2^2\cdot 3\cdot 5 \\ 35=5\cdot 7 \\ LCM(1,60,35)=2^2\cdot 3\cdot 5\cdot 7=420 \\ n=LCM(1,60,35)=420 \\ LCD(\frac{1}{1},\frac{45}{60},\frac{45}{35})=n \\ \frac{1}{1}=\frac{420}{420} \\ \frac{45}{60}=\frac{315}{420} \\ \frac{45}{35}=\frac{540}{420} \\ 420k+315k+540k<84000 \\ 1275k<84000 \\ 17k<1120 \\ {k}_0=1120/17=\frac{1120}{17}=65\frac{15}{17}\doteq 65.8824 \\ {x}_1=28+21+36=85 \\ {x}_2=56+42+72=170 \end{gathered}$$

Try another example