# In 15 years, Maya will be twice as old as David is now. In 15 years, David will be as old as Maya will be 10 years from now. How old are they now?

May 3, 2018

Maya is 25, David is 20.

#### Explanation:

Let's use x for Maya's age, and y for David's.

From the first sentence we can equate that to $x + 15 = 2 y$
From the second sentence we can equate that $y + 15 = x + 10$

We can isolate a variable to find it's value in terms of the other variable. For this we will use the second equation, giving us:

$y = x + 10 - 15$
$y = x - 5$

We'll use this new value in the first equation:

$x + 15 = 2 \left(x - 5\right)$
$x + 15 = 2 x - 10$
$15 = x - 10$
$x = 25$

Given our x value, we can apply it to any equation to find y. We'll use the second.

$y + 15 = 25 + 10$
$y + 15 = 35$
$y = 20$

Remember x = Maya's age, so she is 25; y = David's age, so he is 20.