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If x and y are positive integers for which 3x + 2y + xy = 115 + 7x, then what is x + y?

 Oct 19, 2021
 #1
avatar+390 
0

Hello Guest,

 

here's the answer:

 

\(3x+2y+xy=115+7x\) ,

 

\(\frac{d}{dx}(3x)+\frac{d}{dx}(2y)+\frac{d}{dx}(xy)=\frac{d}{dx}(115)+\frac{d}{dx}(7x)\),

 

\(3+\frac{d}{dx}(2y)+\frac{d}{dx}(xy)=\frac{d}{dx}(115)+\frac{d}{dx}(7x)\),

 

\(3+\frac{d}{dy}(2y)*\frac{dy}{dx}+\frac{d}{dx}(xy)=\frac{d}{dx}(115)+\frac{d}{dx}(7x)\) ,

 

\(3+\frac{d}{dy}(2y)*\frac{dy}{dx}+\frac{d}{dx}(x)*y+x*\frac{d}{dx}(y)=\frac{d}{dx}(115)+\frac{d}{dx}(7x)\) ,

 

\(3+\frac{d}{dy}(2y)*\frac{dy}{dx}+\frac{d}{dx}(x)*y+x*\frac{d}{dx}(y)=0+\frac{d}{dx}(7x)\) ,

 

\(3+2*\frac{dy}{dx}+\frac{d}{dx}(x)*y+x*\frac{d}{dx}(y)=0+\frac{d}{dx}(7x)\) ,

 

\(3+2*\frac{dy}{dx}+1y+x*\frac{d}{dx}(y)=0+\frac{d}{dx}(7x)\) ,

 

\(3+2*​​\frac{dy}{dx}+1y+x*\frac{d}{dx}(y)=0+\frac{d}{dx}(7x)\) ,

 

\(3+2*\frac{dy}{dx}+1y+x*\frac{d}{dy}(y)*\frac{dy}{dx}=0+\frac{d}{dx}(7x)\) ,

 

\(3+2*\frac{dy}{dx}+1y+x*\frac{d}{dy}(y)*\frac{dy}{dx}=\frac{d}{dx}(7x)\) ,

 

\(3+2*\frac{dy}{dx}+1y+x*\frac{d}{dy}(y)*\frac{dy}{dx}=7\) ,

 

\(3+2*\frac{dy}{dx}+y+x*\frac{d}{dy}(y)*\frac{dy}{dx}=7\) ,

 

\(3+2*\frac{dy}{dx}+y+x*1*\frac{dy}{dx}=7\) ,

 

\(3+2*\frac{dy}{dx}+y+x*\frac{dy}{dx}=7\) ,

 

\(2*\frac{dy}{dx}+x*\frac{dy}{dx}=7-3-y\) ,

 

\((2+x)*\frac{dy}{dx}=7-3-y\) ,

 

\((2+x)*\frac{dy}{dx}=4-y\) ,

 

\(\frac{dy}{dx}=\frac{4-y}{2+x}\) ,

 

so the solution is: \(\frac{dy}{dx}=\frac{4-y}{2+x}\) .

 

Straight

 Oct 23, 2021
 #2
avatar+32738 
+2

"If x and y are positive integers for which 3x + 2y + xy = 115 + 7x, then what is x + y?"

 

 Oct 24, 2021

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