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# age problem

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Seven years ago, Grogg's dad was $12$ times as old as Grogg. Three years ago, Grogg's dad was $7$ times as old as Grogg. How old is Grogg's dad currently?

Oct 28, 2023

#1
+423
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To solve the problem, we can use the given information to write down two equations that describe the ages of Grogg and his dad. Let Grogg's current age be g and Grogg's dad's current age be d.

Seven years ago: \begin{align*} d - 7 &= 12(g - 7) \ d &= 12g - 84 + 7 \ d &= 12g - 77 \end{align*}

Three years ago: \begin{align*} d - 3 &= 7(g - 3) \ d &= 7g - 21 + 3 \ d &= 7g - 18 \end{align*}

Now we have two independent equations, and we can solve for our two unknowns. We can start by solving the first equation for d and substituting it into the second equation:

d = 12g - 77 7g - 18 = 12g - 77 -5g = -59 g = 11.8

Now that we know Grogg's age, we can substitute it back into either of our original equations to solve for Grogg's dad's age. Let's substitute it into the first equation:

\begin{align*} d &= 12g - 77 \ d &= 12(11.8) - 77 \ d &= 141.6 - 77 \ d &= \boxed{64.6} \end{align*}

Therefore, Grogg's dad is currently 64.6 years old.

Oct 28, 2023