Question #759bc

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Question #759bc

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Answer 1 · 2016-09-16T00:33:42

$12$ $12$

Explanation:

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

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

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

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

$\Rightarrow A = \frac{A}{2} + 12 - 6$ $=> A = A/2 + 12 - 6$

#=> A=A/2 + 6

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

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

$\Rightarrow \frac{A}{2} = 6$ $=>A/2 = 6$

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

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

$\Rightarrow A = 12$ $=> A = 12$

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

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

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

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Question #759bc

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