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If x and y are integers, what is the smallest possible positive value of 30x + 18y?

 Jan 4, 2020
 #1
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(0,0) lol

 Jan 4, 2020
 #2
avatar+19739 
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If x and y are POSITIVE integers and they are not EQUAL, then

30(1) + 18(2) = 66

 

I think Geno's answer below is best !  (as Q did not specify x and y are positive as I answered)

 Jan 4, 2020
edited by ElectricPavlov  Jan 4, 2020
 #3
avatar+17873 
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Since the value of 30x + 18y must be positive, x=0 and y=0 (which gives an answer of 0) won't fit the criterion.

 

Although the answer must be positive, the values of  x  and  y  don't have to be positive  -- one or both could be negative.

 

Since  30x + 18y  can be factored into  6(5x + 3y), the answer must be divisible by 6.

 

The smallest positive integer divisible by  6  is  6; so the smallest possible answer is 6.

 

You can get  6  various ways; one way is to have  x = 2  and  y = -3.

 Jan 4, 2020

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