equations

 

Seven years ago, Grogg's dad was 6 times as old as Grogg, and 4 years ago, his dad was 4 times as old as Grogg. How old is Grogg's dad currently?  

 

 

Call Grogg's age now "G" and his dad's age now "D"  

 

Seven years ago                           (D – 7)  =  6 * (G – 7)  

Four years ago                              (D – 4)  =  4 * (G – 4)  

 

Multiply them out                            D – 7  =  6G – 42          (eq 1)  

                                                       D – 4  =  4G – 16          (eq 2)  

 

Subtract (eq 2) from (eq 1)                – 3  =  2G – 26  

 

                                                           23  =  2G  

 

                                                             G  =  11.5  

 

Find D by

plugging G back into (eq 1)               D – 7  =  (6)(11.5) – 42 

 

                                                        D – 7  =  69 – 42  

 

                                                              D  =  27 + 7  

 

                                                              D  =  34  

 

Check answer by

plugging G back into (eq 2)                D – 4  =  (4)(11.5) – 16  

 

                                                         D – 4  =  46 – 16 

 

                                                               D  =  30 + 4  

 

                                                               D  =  34 

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