Question

Camille is attending a fundraiser. She pays for her admission and buys raffle tickets for \$5$5 each. If she buys 1010 raffle tickets, then she would spend a total of \$135$135 at the fundraiser. The number SS of dollars Camille spends at the fundraiser is a function of rr, the number of raffle tickets she buys. Write the function's formula.

Answer 1

`S=5r+85`

Explanation:

Let S represent the number of dollars Camille spends at the fundraiser and r represent the number of raffle tickets she buys.

We will write our function in slope-intercept form of equation:
`y=mx+b`, where m represents the slope and b represents y-intercept.

We have been given that Camille pays for her admission and buys raffle tickets for $5 each, so the cost of r tickets will be 5r.

As with each increase in number of tickets (r), the amount Camille spends at fundraiser (S) will increase by 5, so slope of our line will be 5.

We are also told that if she buys 10 raffle tickets, then she would spend a total of $135 at the fundraiser. This means at r equals 10, S will be 135.

Let us substitute m=5 and the coordinates of point (10,135) in slope-intercept form of equation to find y-intercept of our line.
`135=5*10+b`

`135=50+b`

Let us subtract 50 from both sides of our equation.

`135-50=50-50+b`

`85=b`

Let us substitute our slope and y-intercept in slope-intercept form of equation to get our desired function.

`S=5r+85`

Therefore, the function
`S=5r+85` gives the number S of dollars Camille spends at the fundraiser is a function of r, the number of raffle tickets she buys.