# 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?

Sep 20, 2015

Maya is 25 years old, and David is 20 years old, now.

#### Explanation:

Let "m" be the age of Maya, and
"d" the age of David, now at the present.

There are two key sentences in the question.

First sentence:
"In 15 years, Maya will be twice as old as David is now."

The words "In 15 years, Maya will be..." translates to "adding 15 to the present".
That is, in 15 years, Maya's age will be:
$m + 15$ (years old)

Then they say "will be twice as old as David is now."
The key term here is "now".
(Note: if the word "now" wasn't mentioned, you would not know if David's age is "David's age now" or "David's age in 15 years". )
The age of David now is "d", as we said in the beginning.

They say "twice as old", which means "two times", so this part can be written:
$2 \cdot d$ (years old)

That is, we can then write the sentence as the following equation:
$m + 15 = 2 \cdot d$

Second sentence:
"In 15 years, David will be as old as Maya will be 10 years from now."

Again, the "In 15 years, David will be..." translates to:
$d + 15$ (years old)
then they continue "...as old as Maya will be 10 years from now."
The part "as old as" means it is going to be the same (equal).

Again, the keyword here is "from now."
10 years from now Maya will be:
$m + 10$ (years old)
So the equation is:
$d + 15 = m + 10$

Solving the equations
We have:
$m + 15 = 2 d$
and
$d + 15 = m + 10$

Subtracting the two equations, we get:
$\left(m + 15\right) - \left(m + 10\right) = 2 d - \left(d + 15\right)$
so
$5 = d - 15$
that is:
$d = 20$
and substituting this back into the first equation we get:
$m + 15 = 2 \cdot 20 = 40$
so
$m = 25$

Conclusion: Maya is 25 years old, and David is 20 years old, now.