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Seven years ago, Grogg's dad was 8 times as old as Grogg, and 4 years ago, his dad was 5 times as old as Grogg. How old is Grogg's dad currently?

 

I'm pretty sure im supposed to start by giving variables... but i'm not sure what to do after that 

 May 29, 2023
 #1
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Let g = Grogg's age and d = Grogg's dad's age.

7 years ago, Grogg's dad was 8 times as old as Grogg:

d - 7 = 8(g - 7)

4 years ago, his dad was 5 times as old as Grogg:

d - 4 = 5(g - 4)

Solving for g and d, we get:

g = 11 d = 44

Therefore, Grogg's dad is currently 44 years old.

 May 29, 2023
 #2
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d - 7 = 8(g - 7)..........................(1)    

d - 4 = 5(g - 4)..........................(2), solve for d, g

 

Use substitution to get:

 

g ==11 years old

d==39 years old

 May 29, 2023
 #3
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Let Grogg's age be g and his dad's age be d. We can set up a system of equations to represent the information given in the problem:

Seven years ago, Grogg's dad was 8 times as old as Grogg: d−7=8(g−7)

Four years ago, his dad was 5 times as old as Grogg: d−4=5(g−4)

We can solve this system of equations by substitution. First, we can solve the first equation for g:

g=8d−7​+7

We can then substitute this value of g into the second equation:

d−4=5(8d−7​+4)

We can then solve this equation for d:

d=30

Therefore, Grogg's dad is currently 30 years old.

 May 30, 2023
 #4
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 d−4=5(g−4)................(1)

d==5(g - 4) + 4

 

d−7=8(g−7)................(2)

5(g - 4) + 4 - 7==8(g - 7)

5g - 20 + 4 - 7==8g - 56

56 - 20 + 4 - 7==8g - 5g

33 == 3g

g==33/3==11 - sub this into (2) above

 

d - 7==8(11 - 7)

d - 7 ==32

d ==32 + 7 ==39 years - his dad's current age.

Guest May 30, 2023
 #5
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Grogg's age 7 years ago = x Grogg's dad's age 7 years ago = 8x Grogg's age 4 years ago = x+3 Grogg's dad's age 4 years ago = 5(x+3)

8x+7 = 5(x+3) + 4 3x = 8 x = 8/3

Grogg's dad's age now = 8x+7 = 8(8/3) + 7 = 31

So the answer is 31

 May 30, 2023
 #6
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We can use the given information to set up a system of equations to solve for Grogg's and his dad's current ages. Let g be Grogg's current age and d be his dad's current age. We know that 7 years ago, Grogg's dad was 8 times as old as Grogg, so we have the equation d−7=8(g−7). We also know that 4 years ago, Grogg's dad was 5 times as old as Grogg, so we have the equation d−4=5(g−4). We can solve this system of equations by first multiplying the second equation by 8 and then subtracting the first equation from the second equation. This gives us the equation 7d−28=35g−160. We can then divide both sides of this equation by 7 to get d−4=5g−23. Finally, we can add 4 to both sides of this equation to get d=5g−19.

Now that we know the relationship between Grogg's and his dad's ages, we can plug in the given information to solve for Grogg's current age. We know that 7 years ago, Grogg's dad was 8 times as old as Grogg, so we have the equation d−7=8(g−7). Plugging in d=5g−19, we get 5g−26=8(g−7). We can then solve for g to get g=13.

Now that we know Grogg's current age is 13, we can plug it into the equation d=5g−19 to solve for his dad's current age. This gives us d=5(13)−19=46. Therefore, Grogg's dad is currently 46 years old.

 May 30, 2023

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