At the holiday valley ski resort, skis cost $16 to rent and snowboards cost $19. If 28 people rented on a certain day and the resort brought in $478, how many skis and snowboards were rented?

If a total of [tex]28[/tex] people rented on a certain day, then the total number of skis and snowboards rented that particular day is also [tex]28[/tex].

This gives us the equation

[tex]x+y=28...eqn(1)[/tex].

If skis cost $ [tex]16[/tex], then [tex]x[/tex] number of skis cost $ [tex]16x[/tex].

If snowboards cost $ [tex]19[/tex], then [tex]y[/tex] number of snowboards cost $ [tex]19y[/tex].

The total cost will give us another equation,

[tex]16x+19y=478...eqn(2)[/tex]

From equation (1),

[tex]y=28-x...eqn(3)[/tex].

We put equation (3) into equation (2) to get,

[tex]16x+19(28-x)=478[/tex]

We expand the brackets to obtain,

[tex]16x+532-19x=478[/tex]

We group like terms to get,

[tex]16x-19x=478-532[/tex]

This implies that,

[tex]-3x=-54[/tex]

We divide both sides by [tex]-3[/tex] to get,

[tex]x=18[/tex]

We put [tex]x=18[/tex] into equation (3) to get,

[tex]y=28-18[/tex]

[tex]y=10[/tex]

Therefore [tex]18[/tex] skis and [tex]10[/tex] snowboards were rented.