Answer
The equation specified by the problem is:
$$\frac{2x}{5} + \frac{x}{4} = 13$$
The solution is:
$$x = 20$$
Work Step by Step
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 $13$:
$$x = 20$$
