Camille is attending a fundraiser. She pays for her admission and buys raffle tickets for

Question

\[\$5\] each. If she buys
\[10\] raffle tickets, then she would spend a total of
\[\$135\] at the fundraiser.
The number
\[S\] of dollars Camille spends at the fundraiser is a function of
\[r\], the number of raffle tickets she buys.
Write the function's formula.
\[S=\]

Answer 1

Let \( A \) be the admission cost. Camille buys \( r \) raffle tickets, each costing $5. Therefore, the amount she spends on raffle tickets is \( 5r \).

The total amount \( S \) that Camille spends at the fundraiser can be expressed as the sum of the admission cost and the cost of the raffle tickets:

\[ S = A + 5r \]

When Camille buys 10 raffle tickets, her total spending is $135. Thus, we can set up the equation:

\[ 135 = A + 5 \times 10 \]

Calculating the cost of 10 raffle tickets:

\[ 5 \times 10 = 50 \]

Now substituting this into the equation:

\[ 135 = A + 50 \]

To find the admission cost \( A \):

\[ A = 135 - 50 = 85 \]

Now we have determined that the admission cost is $85. We can substitute \( A \) back into the function to find \( S \):

\[ S = 85 + 5r \]

Thus, the formula for the function \( S \) in terms of \( r \) is:

\[ S = 85 + 5r \]