An elevator has a capacity of 12 ~adults or 20 ~children. How many...

As per the question :

Let the weight of one adult & $= x$

And the weight of one child ~$= y$

Then, total capacity $= 12 \times x = 20 \times y$

$⇒ y = \dfrac{3x}{5}$~

Let $A$ be the number of adults that board the elevator with $15$ children.

According to the question :~

$15y + Ax = 12x$
~
$15 \times \dfrac{3x}{5} + A \times x = 12 \times x$

$⇒ 9x + Ax = 12x$

$⇒ 9 + A = 12$

$⇒ A = 3$

Hence, $3$ adults can board the elevator with $15$ children.