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Michael is 4 times as old as Brandon and is also 27 years older than Brandon.
How old is Brandon?

Michael is \(4\) times as old as Brandon and is also \(27\) years older than Brandon. $\newline$ How old is Brandon?

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Solve a system of equations using any method: word problems

Full solution

Q. Michael is \(4\) times as old as Brandon and is also \(27\) years older than Brandon.

\newline

How old is Brandon?

Equation $1$ : Michael's age in terms of Brandon's age: Let's denote Brandon's age as $B$ and Michael's age as $M$ . According to the problem, Michael is $4$ times as old as Brandon, which gives us the first equation: $\newline$ $M = 4B$
Equation $2$ : Michael's age in terms of Brandon's age and the age difference: The problem also states that Michael is $27$ years older than Brandon, which gives us the second equation: $\newline$ $M = B + 27$
System of Equations: Now we have a system of two equations: $\newline$ $1$ ) $M = 4B$ $\newline$ $2$ ) $M = B + 27$ $\newline$ We can set these two equations equal to each other since they both equal $M$ . $\newline$ $4B = B + 27$
Setting the Equations Equal: Next, we solve for $B$ by subtracting $B$ from both sides of the equation: $\newline$ $4B - B = B + 27 - B$ $\newline$ $3B = 27$
Solving for Brandon's Age: Now, we divide both sides by $3$ to find the value of B: $\newline$ $\frac{3B}{3} = \frac{27}{3}$ $\newline$ $B = 9$

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