# Question 759bc

Sep 16, 2016

$12$

#### Explanation:

Let $A$ represent Rico's age. If we write out the process of adding $24$ to $A$, then dividing by $2$, then subtracting $6$, and setting that result as equal to $A$ in algebraic notation, we get

$A = \frac{A + 24}{2} - 6$

We now wish to solve for $A$. First, we use the fact that
$\frac{a + b}{c} = \frac{a}{c} + \frac{b}{c}$
(this is effectively using the distributive property on $\frac{1}{c} \left(a + b\right)$).

$A = \frac{A}{2} + \frac{24}{2} - 6$

$\implies A = \frac{A}{2} + 12 - 6$

=> A=A/2 + 6

Next, we gather all terms which include $A$ on one side of the equation by subtracting $\frac{A}{2}$ from both sides.

$A - \frac{A}{2} = 6$

$\implies \frac{A}{2} = 6$

Finally, we multiply by $2$ to remove the coefficient of $\frac{1}{2}$ from the $A$ term.

$\frac{A}{2} \cdot 2 = 6 \cdot 2$

$\implies A = 12$

It is also good practice to check the final answer by plugging it into the original problem:

$\frac{12 + 24}{2} - 6 = \frac{36}{2} - 6 = 18 - 6 = 12$

As that checks out, we now know that Rico is $12$