Question

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?

Answer 1

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

Explanation:

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!)