Melanie is raising money for a school trip by selling candy bars and bags of chips. The price of each candy bar is $1.50 and the price of each bag of chips is $1.25. Yesterday Melanie made $33.25 and sold 13 more candy bars than bags of chips. Determine the number of candy bars sold and the number of bags of chips sold.

Let's denote the number of bags of chips sold as $x$. According to the problem, Melanie sold 13 more candy bars than bags of chips, so the number of candy bars sold is $x + 13$.

The price of each candy bar is $1.50, and the price of each bag of chips is$1.25. Therefore, the total revenue from selling candy bars is $1.50(x + 13)$, and the total revenue from selling bags of chips is $1.25x$.

The total revenue from both candy bars and bags of chips is given as $33.25. We can set up the following equation to represent this:

$1.50(x + 13) + 1.25x = 33.25$

Now, let's solve this equation step by step.

1. Distribute the 1.50 in the first term: $1.50x + 19.50 + 1.25x = 33.25$

2. Combine like terms: $2.75x + 19.50 = 33.25$

3. Subtract 19.50 from both sides to isolate the term with $x$: $2.75x = 13.75$

4. Divide both sides by 2.75 to solve for $x$: $x = \frac{13.75}{2.75}$ $x = 5$

So, Melanie sold 5 bags of chips.

To find the number of candy bars sold, we use the relationship $x + 13$: $x + 13 = 5 + 13$ $x + 13 = 18$

Therefore, Melanie sold 18 candy bars and 5 bags of chips.