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help plz

0
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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
+390
0

Hello Guest,

$$3x+2y+xy=115+7x$$ ,

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$(2+x)*\frac{dy}{dx}=7-3-y$$ ,

$$(2+x)*\frac{dy}{dx}=4-y$$ ,

$$\frac{dy}{dx}=\frac{4-y}{2+x}$$ ,

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

Straight

Oct 23, 2021
#2
+32738
+2

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

Oct 24, 2021