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If \(0.8= \frac{y}{186+x}\), find the smallest value of x, if x and y are positive integers.

 May 11, 2023
 #1
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Multiply both sides of the equation by 186 + x to get 148.8 + 0.8x = y. Subtract 148.8 from both sides to get 0.8x = y - 148.8. Divide both sides by 0.8 to get x = (y - 148.8) / 0.8. Since x and y are positive integers, y - 148.8 must be divisible by 8. The smallest value of y - 148.8 that is divisible by 8 is 8, so y = 156.8. The smallest value of x is therefore (156.8 - 148.8) / 0.8 = 8. So the answer is 8

 May 11, 2023
 #2
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0.8 = y/(186 + x),

148.8 + 0.8x = y.

 y is to be an integer, so 0.8x has to be something point 2.

The smallest value of that fits is x = 4, then 148.8 + 3.2 =152.

 May 11, 2023

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