## Introductory Algebra for College Students (7th Edition)

The equation specified by the problem is: $$\frac{2x}{5} + \frac{x}{4} = 13$$ The solution is: $$x = 20$$
We set up this equation by translating different portions of the statement from words to algebraic terms: "Two-fifths of a number" is "$\frac{2x}{5}$" "One-fourth of a number" is "$\frac{x}{4}$" "The sum is $13$" is translated to mean that you need to add these two fractions together to get $13$. We put all the portions together to get: $$\frac{2x}{5} + \frac{x}{4} = 13$$ To get rid of the fractions, we multiply by the least common denominator of all the fractions. In this case, the least common denominator is $20$. $$20(\frac{2x}{5}) + 20(\frac{x}{4}) = 20(13)$$ We divide out common factors to get rid of the fractions: $$8x + 5x = 260$$ Combining like terms, we get: $$13x = 260$$ Divide both sides by $13$: $$x = 20$$