Question

A ski club with 28 members went on a ski trip. some members rented skis and the rest rented snowboards. if skis rent for $16.00 a day and snowboards rent for $19.00 a day, and the club spent 478.00 in rentals, how many ski club members rented skis?

Answer 1

16 skis and 18 snowboards were rented.

Explanation:

Let the number of skis rented be and the number of snowboards rented be .

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

This gives us the equation

.

If skis cost $ , then number of skis cost $ .

If snowboards cost $ , then number of snowboards cost $ .

The total cost will give us another equation,

From equation (1),

.

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

We expand the brackets to obtain,

We group like terms to get,

This implies that,

We divide both sides by to get,

We put into equation (3) to get,

Therefore skis and snowboards were rented.

Answer 2

`there \ are \ 28 \ members \\ the \ number \ of \ members \ renting \ skis - x\\the \ number \ of \ members \ renting \ snowboards - y\\skis \ rent \ for \ \$16.00 \ a \ day \ and \ snowboards \ rent \ for \ \$19.00 \ a \ day\\\\\begin{cases} x+y=28 \ \ / \cdot (-16) \\ 16x+19y = 478 \end{cases}`


`\begin{cases} -16x-16y=-448 \\ 16x+19y = 478 \end{cases}\\+ -------\\3y=30 \ \ / :3 \\y=10 \\ \\ x+y=28\\x+10=28\\x=28-10\\x=18 \\ \\ Answer: \ 18 \ members \ rented \ skis .`