Juan is 5 years older then John. Six years ago the sum of their ages was 25. How old are they now?
NOW:
John --- x
Juan --- x+5
6 years ago:
John --- x-6
Juan --- x+5-6 = x-1
x+5 + x-1 = 25
take over
To find the current ages of Juan and John, we can set up a system of equations based on the given information.
Let's assume John's current age is x years. As Juan is 5 years older than John, Juan's current age would be (x + 5) years.
According to the second piece of information, six years ago, the sum of their ages was 25. So, let's subtract 6 years from their current ages and form an equation:
(x - 6) + ((x + 5) - 6) = 25
Now, let's simplify the equation:
x - 6 + (x - 1) = 25
2x - 7 = 25
Next, isolate the variable:
2x = 25 + 7
2x = 32
Finally, divide both sides by 2 to solve for x:
x = 32 / 2
x = 16
John's current age is 16 years. Since Juan is 5 years older, his current age is:
(x + 5) = (16 + 5) = 21
Therefore, John is 16 years old, and Juan is 21 years old.