Joanie runs the concession stand for the school's baseball games. At each game, the best selling items are pretzels and hot dogs. Pretzels are $3 each, and hot dogs are $2 each. Today she sold 15 more hot dogs than pretzels and made $195 in total sales. Use a system of equations to model the situation above, and determine which of the following are possible amounts of pretzels and hot dogs that Joanie sold today ? A. 35 pretzels, 45 hot dogs B. 15 pretzels, 30 hot dogs C. 31 pretzels, 51 hot dogs D. 33 pretzels, 48 hot dogs

To solve this problem, we need to create two equations based on the information given. Let's call the number of pretzels sold "p" and the number of hot dogs sold "h".

According to the first piece of information, pretzels are $3 each, and hot dogs are $2 each. Also, the total amount of money made from selling pretzels and hot dogs is $195. This can be modeled by the equation:

[ 3p + 2h = 195 \]

The second piece of information tells us that Joanie sold 15 more hot dogs than pretzels. This can be modeled by the equation:

[ h = p + 15 \]

We now have a system of equations:

[ \begin{cases} 3p + 2h = 195 \\ h = p + 15 \end{cases} \]

We can now substitute the second equation into the first one to find the number of pretzels sold:

[ 3p + 2(p + 15) = 195 \] \[ 3p + 2p + 30 = 195 \] \[ 5p + 30 = 195 \] \[ 5p = 195 - 30 \] \[ 5p = 165 \] \[ p = 165 / 5 \] \[ p = 33 \]

Now that we have the number of pretzels, we can find the number of hot dogs:

[ h = 33 + 15 \] \[ h = 48 \]

So Joanie sold 33 pretzels and 48 hot dogs. Looking at the options given, D. 33 pretzels, 48 hot dogs is the correct one.