At the Holiday Valley Ski Resort, skis cost $16 to rent and snowboards cost $19. If 28 peopie rented on a certain day and the resort brought in $478, how many skis and snowboards were rented?

There were ##18## skiers and ##10## snowborders.

Assume, there were ##X## skis and ##Y## snowboards rented. Since there were ##28## people who rented equipment, we have the first equation: ##X+Y=28##

Considering the price of ##$16## per ski and ##$19## per snowboard, and the total amount resort has got is ##$478##, we have the second equation: ##16X+19Y=478##

To solve this system of two linear equations with two unknowns, we will use the method of substitution - resolve the first equation for ##Y## in therms of ##X## and substitute it into the second equation, thus getting one equation with one unknown.

From the first equation, adding ##-X## to both sides, we get: ##-X+X+Y=-X+28## or, cancelling ##-X+X## because it's equal to 0, ##Y=-X+28=28-X##

Substitute this expression for ##Y## into the second equation: ##16X+19(28-X)=478## Using distributive law ##a(b+c)=ab+ac##, the latter is: ##16X+19*28-19X=478## Using commutative law of addition, we can change the sequence of operation. Also, perform the multiplication: ##16X-19X+532=478##

Using the distributive law, we can combine ##16X-19X##: ##(16-19)X+532=478##

Subtract ##478## from both sides of this equation and perform ##16-19## operation: ##-3X+532-478=478-478## or ##-3X+54=0## Adding ##3X## to both sides yields: ##3X-3X+54=3X## or ##54=3X##

Dividing by ##3## both sides of this equation, ##18=X##

From this we can find ##Y=-X+28##: ##Y=-18+28=10##

CHECKING: ##18## (skis) ##+## ##10## (snowboards) = ##28## (CHECK!) ##18*$16= $288## (skis total) ##10*$19=$190## (snowboards total) ##$288+$190=$478## (total rent) (CHECK!)