age problem

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.