Solution for #16

Let g be the total units of grass in the field before the sheep are turned out. Let s be the number of units of grass each sheep eats per day. We must determine the constant values of g and r from the information given in the problem. The total number of grass units eaten equals the number of days times the amount of grass the sheep eat per day. From this, we can construct two equations:

        g + 20r = 20(10s)
        g + 10r = 10(15s) 

Reducing the equations, we obtain:

        g + 20r = 200s
        g + 10r = 150s 

Subtract one equation from the other:

        10r = 50s 

So r equals 5s. Substituting back, we discover g equals 100s. Now we construct an equation for the case of having 25 sheep turned out in the field, where x is the number of days it takes the sheep to eat all the grass:

        g + xr = x(25s)
        100s + x(5s) = x(25s)
        20sx = 100s
        x = 5 

So 25 sheep would consume all the grass in the field in 5 days.