Aaron is 21 years younger than Ryan. In 5 years Ryan will be twice as old as Aaron. How old are they now?
Let A be Aaron's age, and R be Ryan's age (current).
Thus we're given:
A = R-21
2(A+5) = R+5
Solve these simultaneous equations.
To solve this problem, let's break it down step by step.
Let's assume Aaron's current age is 'A' and Ryan's current age is 'R'.
We know that "Aaron is 21 years younger than Ryan," so we can write the equation: A = R - 21.
We also know that "In 5 years, Ryan will be twice as old as Aaron," so we can write the equation: (R + 5) = 2(A + 5).
Now we have a system of two equations:
1) A = R - 21
2) (R + 5) = 2(A + 5)
To solve this system, we can substitute the value of A from the first equation into the second equation.
Substituting A = R - 21 in the second equation gives: (R + 5) = 2(R - 21 + 5).
Simplifying the equation gives: R + 5 = 2(R - 16).
Expanding the right side of the equation gives: R + 5 = 2R - 32.
Now, let's solve for R:
R - 2R = -32 - 5
-R = -37
R = 37.
Now that we know Ryan's current age is 37, we can substitute this value in the first equation to find Aaron's age.
A = R - 21
A = 37 - 21
A = 16.
Therefore, Aaron is currently 16 years old and Ryan is currently 37 years old.