Question

the numerator of a certain fraction is four times the denominator. If 10 is added to both numerator and denominator the resulting fraction is equivalent to 2. What is the original fraction?

Answer 1

Okay so will have x be the denominator. 
Numerator: 4x
Fraction: $\frac{4x}{x}$ which would be equivalent to 4.
If you add 10 to both the numerator and denominator the resulting fraction is
$\frac{4x + 10}{x + 10}= 2$
We multiply both sides of the equal side sign times (x + 10) we get...
4x + 10 = 2 * (x + 10)
4x + 10 = 2x + 20
4x - 2x = 20 - 10
2x = 10
x = 5 < denominator
4x = 4 * 5 = 10 < So the fraction is 10/5