Question: Casey has a small business making dessert baskets. She estimates that her fixed weekly costs for rent and electricity are $200. The ingredients for one dessert basket cost $2.50. If Casey made 40 baskets this past week, what were her total weekly costs? Her total costs for the week before were $562.50. How many dessert baskets did she make the week before?
1. **State the problem:**
Casey has fixed weekly costs of $200 and variable costs of $2.50 per dessert basket. We want to find her total weekly costs for 40 baskets and determine how many baskets she made the previous week given total costs of $562.50.
2. **Write the formula:**
The total cost $C$ is given by the linear equation:
$$C = 2.50x + 200$$
where $x$ is the number of baskets made.
3. **Calculate total costs for 40 baskets:**
Substitute $x = 40$:
$$C = 2.50 \times 40 + 200$$
$$C = 100 + 200$$
$$C = 300$$
So, the total weekly costs for 40 baskets is $300$.
4. **Find number of baskets made the previous week:**
Given total costs $C = 562.50$, solve for $x$:
$$562.50 = 2.50x + 200$$
Subtract 200 from both sides:
$$562.50 - 200 = 2.50x$$
$$362.50 = 2.50x$$
Divide both sides by 2.50:
$$\frac{362.50}{\cancel{2.50}} = \frac{2.50x}{\cancel{2.50}}$$
$$145 = x$$
5. **Answer:**
- Total weekly costs for 40 baskets: $300$
- Number of baskets made the previous week: $145$