Meadow

On the meadow grazing horses, cows and sheep, together 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 equall. How many
horses, cows and sheep are on the meadow together?

Result

x1 =  85
x2 =  170

Solution:

x = a+b+c < 200
b = 45/60 a
c = 45/35 a
a + 45/60 a + 45/35 a < 200
LCD(1⁄1, 45⁄60, 45⁄35) = LCM(1, 60, 35) = 22×3×5×7 = 420
1⁄1 = 420⁄420
45⁄60 = 315⁄420
45⁄35 = 540⁄420


420 k + 315 k + 540 k < 84000
1275 k < 84000
17 k < 1120

x = 56+42+72 = 170
x = 28+21+36 = 85


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