What number can be added to both the numerator and denominator of $\frac{3}{5}$ so that the resulting fraction will be equivalent to $\frac{5}{6}$?
I need to find a number x that satisfies the equation $\frac{3 + x}{5 + x} = \frac{5}{6}$. I can cross-multiply to get rid of the fractions: $(3 + x) \cdot 6 = (5 + x) \cdot 5$. Expanding the brackets, I get $18 + 6x = 25 + 5x$. Subtracting $5x$ and $18$ from both sides, I get $x = 7$. To check, I can plug in x = 7 into the original equation and see if it is true: $\frac{3 + 7}{5 + 7} = \frac{10}{12} = \frac{5}{6}$, which is correct. 