#### Answer

The equation we set up is:
$$\frac{x}{3} + \frac{x}{5} = 16$$
The solution is:
$$x = 30$$

#### Work Step by Step

To set up the equation, we need to understand the terminology of the statement.
"One-third of a number" can be translated to "$\frac{1}{3}x$"
"One-fifth of a number" can be translated to "$\frac{1}{5}x$"
The statement wants these two fractions to be added together, and the result would be $16$.
We can then set up the following equation:
$$\frac{1x}{3} + \frac{1x}{5} = 16$$
Multiply by the least common denominator to get rid of the fractions. The least common denominator is $15$.
$$15(\frac{1x}{3}) + 15(\frac{1x}{5}) = 15(16)$$
Divide out common factors to get:
$$5x + 3x = 240$$
Combine like terms:
$$8x = 240$$
Solve for $x$:
$$x = 30$$