Question

Aaron and Maria collected shells one morning at the beach. Maria had 3 times as many as Aaron, but they would have had the same number of shells if Aaron had found 8 more and Maria had found 6 less. How many shells did Aaron collect?

Answer 1

Let the amount of shells collected by Aaron be $x$ and the amount of shells collected by Maria be $y$ respectively. Then the following system of equations should be solved:
$\left \{ {{3x=y} \atop {x+8=y-6}} \right.$

First of all, express $y$ out of first equation:
$y=3x$

Then, replace $y$ in second equation with found expression and solve it:
$x+8=3x-6$
$2x=14$
$x=14/2=7$

Finally, replace $x$ in first equation with found value and solve it too:
$3*7=y$
$y=21$

So, Aaron has found 7 shells while Maria has found 21.