(2 + frac{3}{x}) times (y + frac{1}{2}) = fra | vedclass

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Question

(C) Given the equation: $(2 + \frac{3}{x}) 	imes (y + \frac{1}{2}) = \frac{31}{4}$.Expanding the expression: $(\frac{2x+3}{x}) 	imes (\frac{2y+1}{2}

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$(14, 3)$

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(C) Given the equation: $(2 + \frac{3}{x}) 	imes (y + \frac{1}{2}) = \frac{31}{4}$.Expanding the expression: $(\frac{2x+3}{x}) 	imes (\frac{2y+1}{2}) = \frac{31}{4}$.This simplifies to: $\frac{(2x+3)(2y+1)}{2x} = \frac{31}{4}$.Cross-multiplying: $4(2x+3)(2y+1) = 62x$,which reduces to $2(2x+3)(2y+1) = 31x$.For $x=14$: $2(2(14)+3)(2y+1) = 31(14) \Rightarrow 2(31)(2y+1) = 31(14)$.Dividing both sides by $62$: $2y+1 = 7 \Rightarrow 2y = 6 \Rightarrow y = 3$.Thus,the values are $x=14$ and $y=3$.

$(2 + \frac{3}{x}) \times (y + \frac{1}{2}) = \frac{31}{4}$,find the values of $x$ and $y$ if $x$ and $y$ are positive integers.

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