Seven years ago, Grogg's dad was 6 times as old as Grogg, and 2 years ago, his dad was 4 times as old as Grogg. How old is Grogg's dad currently?
Let's solve this step-by-step:
Let's assume Grogg's current age is 'x' years.
Seven years ago, Grogg's age would have been (x-7) years.
According to the given information, Grogg's dad was 6 times as old as Grogg seven years ago. So, Grogg's dad's age would have been 6 * (x-7) years.
Two years ago, Grogg's age would have been (x-2) years.
According to the given information, Grogg's dad was 4 times as old as Grogg two years ago. So, Grogg's dad's age would have been 4 * (x-2) years.
Now, let's set up an equation based on the above information:
6 * (x-7) = 4 * (x-2)
Now, let's solve this equation step-by-step:
6x - 42 = 4x - 8 (Expand the brackets)
6x - 4x = 42 - 8 (Combine like terms)
2x = 34 (Simplify)
x = 17 (Divide both sides by 2)
Therefore, Grogg's current age is 17 years.
To find Grogg's dad's age currently, we need to add 7 years to Grogg's current age:
Grogg's dad's age = Grogg's current age + 7
Grogg's dad's age = 17 + 7
Grogg's dad's age = 24
So, Grogg's dad is currently 24 years old.
Let's use algebra to solve the problem.
Let G = Grogg's current age.
Let D = Grogg's dad's current age.
Seven years ago, we know that:
D - 7 = 6(G - 7)
Simplifying:
D - 7 = 6G - 42
D = 6G - 35
Two years ago, we know that:
D - 2 = 4(G - 2)
Simplifying:
D = 4G
Now we can set these two expressions for D equal to each other and solve for G:
6G - 35 = 4G
2G = 35
G = 17.5
Therefore, Grogg is currently 17.5 years old.
To find Grogg's dad's age, we can substitute this value of G back into one of the expressions for D:
D = 6G - 35
D = 6(17.5) - 35
D = 77.
Therefore, Grogg's dad is currently 77 years old.