Question 1209080: Seven years ago, Grogg's dad was 9 times as old as Grogg. Three years ago, Grogg's dad was 2 times as old as Grogg. How old is Grogg's dad currently?
Found 3 solutions by math_tutor2020, MathTherapy, ikleyn:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
| 7 years ago | 3 years ago | | Grogg’s age | x | x+4 | | The dad’s age | 9x | 2(x+4) = 2x+8 |
7 years ago, Grogg's age was x years old.
His dad's age was 9x since its 9 times that of his son's age.
Fast forward 4 years so we arrive at the "3 years ago" timestamp.
At this point Grogg was x+4 years old and his dad was twice his age, so the dad was 2(x+4) = 2x+8 years old.
7 years ago the dad was 9x years old.
3 years ago the dad was 2x+8 years old.
This is a gap of 4 years, so subtracting these previous ages should get us 4.
(2x+8) - 9x = 4
Solving this equation leads to x = 4/7 = 0.571429 approximately
Since this isn't a whole number, there might be a typo somewhere in your question.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
Seven years ago, Grogg's dad was 9 times as old as Grogg. Three years ago, Grogg's dad was 2 times as old as Grogg.
How old is Grogg's dad currently?
That other person made things so COMPLEX. All he had to do was keep the ages CURRENT/"in-the-now", as was requested. What sense
does it make to solve for past ages when current ages are required? Inquiry minds want to know!!
Let Grogg's and his Dad's ages, be G and D, respectively
As such, 7 years ago, the Dad and Grogg were D - 7 and G - 7, respectively
Likewise, 3 years ago, the Dad and Grogg were D - 3 and G - 3, respectively
Then we get: D - 7 = 9(G - 7)____D - 7 = 9G - 63___D - 9G = - 56 ---- eq (i)
Also, D - 3 = 2(G - 3)___D - 3 = 2G - 6___D - 2G = - 3 ---- eq (ii)
Subtracting eq (i) from eq (ii), we get: 7G = 53
Grogg's current age, or G =  or  , which is a NON-INTEGER, and a seemingly NON-SENSICAL answer.
You could have also kept this to one variable: either G for Grogg's age, or D for his Dad's.
Answer by ikleyn(52782)  (Show Source):
You can put this solution on YOUR website! .
As two other tutors explained you, with the given input numbers, the answer is non-integer number,
which for this class of problems is traditionally considered as nonsense.
So, the problem is DEFECTIVE, and there is no sense to go further in more deep explanations.
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Simply throw this defective problem to the closest garbage bin.
It's a great pity for the wasted time.
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