Respuesta :
To find Grogg's dad's current age, let's use algebraic equations to solve the problem.
Let's start by assigning variables. Let G represent Grogg's current age, and let D represent Grogg's dad's current age.
From the first sentence, we know that 7 years ago, Grogg's dad was 9 times as old as Grogg. We can express this as an equation:
\[D - 7 = 9(G - 7)\]
From the second sentence, we know that 4 years ago, Grogg's dad was 6 times as old as Grogg. We can express this as another equation:
\[D - 4 = 6(G - 4)\]
Now, we can solve these two equations to find the values of G and D.
Let's start with the first equation:
\[D - 7 = 9(G - 7)\]
Distributing 9 to (G - 7) gives us:
\[D - 7 = 9G - 63\]
Simplifying further, we have:
\[D = 9G - 63 + 7\]
\[D = 9G - 56\]
Now, let's look at the second equation:
\[D - 4 = 6(G - 4)\]
Distributing 6 to (G - 4) gives us:
\[D - 4 = 6G - 24\]
Simplifying further, we have:
\[D = 6G - 24 + 4\]
\[D = 6G - 20\]
Now, we have two equations for D:
\[D = 9G - 56\]
\[D = 6G - 20\]
Since both equations represent the same value, we can equate them:
\[9G - 56 = 6G - 20\]
Simplifying, we have:
\[3G = 36\]
\[G = 12\]
Now that we know Grogg's age is 12, we can substitute this value back into one of the original equations to find D.
Let's use the equation:
\[D = 9G - 56\]
Substituting G = 12, we have:
\[D = 9(12) - 56\]
\[D = 108 - 56\]
\[D = 52\]
Therefore, Grogg's dad is currently 52 years old.
In summary:
- Grogg is currently 12 years old.
- Grogg's dad is currently 52 years old.
