Meadow

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

Correct answer:

x₁ =  85
x₂ =  170

Step-by-step explanation:

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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