The sum of a fraction and 10 times its reciprocal is 37/4. What is the fraction?
Let that fraction be $$\frac{1}{x}$$
$$ (\frac{1}{x}) + 10x = 37/4$$
$$\Rightarrow (4+40x^{2}) = 37 \times x$$
$$\Rightarrow 40x^{2}-37x+4 = 0$$
$$\Rightarrow(x-\frac{5}{40})(x-\frac{32}{40})=0$$
$$\Rightarrow(x-1/8)(x-\frac{4}{5})=0$$
$$\Rightarrow x = 1/8 or 4/5$$
$$\Rightarrow \text{fraction} = \frac{1}{x} = 8 \text(or) 5/4$$
so the answer is option A.
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