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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+678 
0

Hello Guest,

 

here's the answer:

 

3x+2y+xy=115+7x ,

 

ddx(3x)+ddx(2y)+ddx(xy)=ddx(115)+ddx(7x),

 

3+ddx(2y)+ddx(xy)=ddx(115)+ddx(7x),

 

3+ddy(2y)dydx+ddx(xy)=ddx(115)+ddx(7x) ,

 

3+ddy(2y)dydx+ddx(x)y+xddx(y)=ddx(115)+ddx(7x) ,

 

3+ddy(2y)dydx+ddx(x)y+xddx(y)=0+ddx(7x) ,

 

3+2dydx+ddx(x)y+xddx(y)=0+ddx(7x) ,

 

3+2dydx+1y+xddx(y)=0+ddx(7x) ,

 

3+2dydx+1y+xddx(y)=0+ddx(7x) ,

 

3+2dydx+1y+xddy(y)dydx=0+ddx(7x) ,

 

3+2dydx+1y+xddy(y)dydx=ddx(7x) ,

 

3+2dydx+1y+xddy(y)dydx=7 ,

 

3+2dydx+y+xddy(y)dydx=7 ,

 

3+2dydx+y+x1dydx=7 ,

 

3+2dydx+y+xdydx=7 ,

 

2dydx+xdydx=73y ,

 

(2+x)dydx=73y ,

 

(2+x)dydx=4y ,

 

dydx=4y2+x ,

 

so the solution is: dydx=4y2+x .

 

Straight

 Oct 23, 2021
 #2
avatar+33659 
+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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