<s>[INST] $5 \frac {3}{*} \times 3 \frac {*}{2}=19$? One of my friends gave me this apparently easy-looking problem which I do not know how to crack. The problem is to find the values of   "*" where 
$$5 \frac {3}{*} \times 3 \frac {*}{2}=19\text{ ?}$$ 
I can rearrange the problem as $5 \frac {3}{x} \times 3 \frac {y}{2}=19$ and I have to find the values of $x,y.$  Now $5 \frac {3}{x} \times 3 \frac {y}{2}=19 \implies \frac {5x+3}{x} \times \frac {6+y}{2}=19.$ Now, I do not know which way to  go?
Can someone point me in the right direction? Thanks in advance for your time.
EDIT: Here "*"-s are not same. Infact I know the answer but do not know how to get it. Here $x=7,y=1.$ 
 [/INST] I assume $x, y$ are supposed to be positive integers (otherwise there are infinitely many real solutions for $x, y$). If $y \geq 2$, then $19=(5+\frac{3}{x})(3+\frac{y}{2})>5(3+\frac{2}{2})=20$, a contradiction. Thus $y=1$, so $x=7$.
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