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Seven years ago, Grogg's dad was $9$ times as old as Grogg.  Four years ago, Grogg's dad was $6$ times as old as Grogg. How old is Grogg's dad currently?

 Jan 1, 2024
 #1
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grogg's dad's age = D

Grogg's age = G

 

We can create equations:

(D-7)=9(G-7)

 

and

 

(D-4)=6(G-4)

 

These simplify into 

 

D-7=9G-63

D-4=6G-24

or

 

D=9G-56

D=6G-20

 

Because D equals both of these, we know that 

9G-56=6G-20

 

We solve this and get 

3G=36

G=12. 

 

We can subsitute this into any of the equations.

6(12)-20 = 52

9(12)-56= 52

 

So Grogg's dad is 52 years old.

 

Happy new Year btw :D

 Jan 2, 2024

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