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Algebra Difficulty: Medium

The function $f$ is defined by $f (x) = \frac{x + 15}{5}$ , and $f left parenthesis a right parenthesis equals 10$ , where $a$ is a constant. What is the value of $a$ ?

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Explanation

Choice C is correct. It's given that $f (x) = \frac{x + 15}{5}$ and $f left parenthesis a right parenthesis equals 10$ , where $a$ is a constant. Therefore, for the given function $f$ , when $x = a$ , $f left parenthesis x right parenthesis equals 10$ . Substituting $a$ for $x$ and $10$ for $f (x)$ in the given function $f$ yields $10 = \frac{a + 15}{5}$ . Multiplying both sides of this equation by $5$ yields $50 = a + 15$ . Subtracting $15$ from both sides of this equation yields $35 equals a$ . Therefore, the value of $a$ is $35$ .

Choice A is incorrect. This is the value of $a$ if $f left parenthesis a right parenthesis equals 4$ .

Choice B is incorrect. This is the value of $a$ if $f left parenthesis a right parenthesis equals 5$ .

Choice D is incorrect. This is the value of $a$ if $f left parenthesis a right parenthesis equals 16$ .