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# The numerator of a fraction is 5 less than the denominator. If 6 is added to the...

### Question

The numerator of a fraction is 5 less than the denominator. If 6 is added to the numerator and 4 to the denominator the fraction is doubled. What is the fraction?

### Options

A) $$\frac{2}{7}$$

B) $$\frac{5}{8}$$

C) $$\frac{3}{8}$$

D) $$-\frac{1}{4}$$

### Explanation:

If the numerator be $$x$$, the fraction becomes $$\frac{x}{x+5}$$
Again numerator + 6 and denominator + 4 gives $$\frac{x+6}{x+5+4}$$
Therefore, $$\cfrac{x+6}{x+5+4}=\cfrac{2x}{x+5}$$
Cross multiplying, gives $$2x(x+9)=(x+6)(x+5)$$
$$2x^2+18x=x^2+11x+30$$
Collecting like terms
$$x^2+7x-30=0$$
$$(x+10)(x-3)=0$$
Therefore, $$x+10=0$$ and $$x-3=0$$
$$x=-10$$ and $$x=3$$
At $$x=-10$$, the fraction is $$-\frac{10}{5}$$ and at $$x=3$$, the fraction is $$\frac{3}{8}$$

## Dicussion (1)

• If the numerator be $$x$$, the fraction becomes $$\frac{x}{x+5}$$
Again numerator + 6 and denominator + 4 gives $$\frac{x+6}{x+5+4}$$
Therefore, $$\cfrac{x+6}{x+5+4}=\cfrac{2x}{x+5}$$
Cross multiplying, gives $$2x(x+9)=(x+6)(x+5)$$
$$2x^2+18x=x^2+11x+30$$
Collecting like terms
$$x^2+7x-30=0$$
$$(x+10)(x-3)=0$$
Therefore, $$x+10=0$$ and $$x-3=0$$
$$x=-10$$ and $$x=3$$
At $$x=-10$$, the fraction is $$-\frac{10}{5}$$ and at $$x=3$$, the fraction is $$\frac{3}{8}$$