SOLUTION: karl is 4 years older than danny. eight years ago karl was twice as old as danny. what are their ages now?

Question 386447: karl is 4 years older than danny. eight years ago karl was twice as old as danny. what are their ages now?
Answer by gwendolyn(128) (Show Source): You can put this solution on YOUR website!
We want to determine the ages of Karl and Danny, so we will assign them both variables:
let k= Karl's age
let d= Danny's age
Now, we can use these variables in equations. The problem states that Karl is four years older than Danny. This means that Danny's age plus four is equal to Karl's age. This can be set up as the equation below:
k=d+4
We have two variables, so we need another equation. We also know that eight years ago, Karl's age was two times Danny's age. The way to write this is a little bit more complicated. First, we have to remember that this equation is from "8 years ago." Because of this, both ages have to have 8 subtracted from them. [(k-8); (d-8)] Since Karl's age 8 years ago was twice Danny's age 8 years ago, we can write the equation as below:
k-8=(d-8)*2
Since we know k's value in terms of d, we can substitute it into our second equation:
d+4-8=(d-8)*2
Both halves of the equation can be simplified.
First, we'll distribute the two in the second half of the equation:
d+4-8=d*2-8*2
Then we can multiply the (-8) and 2 in the second half:
d+4-8=d*2-16
After that, we can subtract the 8 from the 4 in the first half:
d-4=2d-16
Now, we can combine the d's to get them on one side.
d-4-d=2d-16-d
-4=d-16
Finally, we can add 16 to both sides to find Danny's age.
-4+16=d-16+16
12=d
Therefore, Danny is 12 years old.
We also need to determine Karl's age. Karl is four years older than Danny, so we can plug Danny's age into that equation:
k=d+4
k=12+4
k=16
So, Karl is 16 years old and Danny is 12 years old.
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