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.