Question
Leroy's Bakery recently spent a total of $90 on new equipment, and their average hourly operating costs are $14. Their average hourly receipts are $44. The bakery will soon make back the amount it invested in equipment. What would the total expenses and receipts both equal? How many hours will that take?
The bakery's expenses and receipts will both total $
after
hours.
The bakery's expenses and receipts will both total $
after
hours.
Answers
GPT-4o mini
To find out how long it will take Leroy's Bakery to break even on the $90 spent on equipment, let's first compute the net profit per hour and then determine how long it will take to cover the initial investment.
1. **Calculate the net profit per hour:**
- Average hourly receipts: $44
- Average hourly operating costs (expenses): $14
- Net profit per hour is calculated as:
\[
\text{Net profit per hour} = \text{Average hourly receipts} - \text{Average hourly operating costs} = 44 - 14 = 30 \text{ dollars}
\]
2. **Determine how long it will take to recover the $90 investment:**
- Investment in equipment: $90
- To find the number of hours (H) it will take to make back this $90, we can set up the equation:
\[
\text{Net profit per hour} \times H = 90
\]
- Plugging in the net profit per hour:
\[
30 \times H = 90
\]
- Solving for \(H\):
\[
H = \frac{90}{30} = 3 \text{ hours}
\]
3. **Calculate total expenses and receipts after 3 hours:**
- Total receipts after 3 hours:
\[
\text{Total receipts} = \text{Average hourly receipts} \times H = 44 \times 3 = 132 \text{ dollars}
\]
- Total expenses after 3 hours:
\[
\text{Total expenses} = \text{Average hourly operating costs} \times H = 14 \times 3 = 42 \text{ dollars}
\]
4. **Total expenses and receipts will both equal:**
- Since the total profit is $90, the total receipts will equal the total expenses plus the profit:
\[
\text{Total receipts} = \text{Total expenses} + 90
\]
But since we calculated the different totals:
- Total receipts = $132
- Total expenses = that plus the original operating costs which will be $132 - $90 = $42.
In conclusion, the total expenses and receipts will both total $132 after 3 hours.
**Final Answer:**
The bakery's expenses and receipts will both total $132 after 3 hours.
1. **Calculate the net profit per hour:**
- Average hourly receipts: $44
- Average hourly operating costs (expenses): $14
- Net profit per hour is calculated as:
\[
\text{Net profit per hour} = \text{Average hourly receipts} - \text{Average hourly operating costs} = 44 - 14 = 30 \text{ dollars}
\]
2. **Determine how long it will take to recover the $90 investment:**
- Investment in equipment: $90
- To find the number of hours (H) it will take to make back this $90, we can set up the equation:
\[
\text{Net profit per hour} \times H = 90
\]
- Plugging in the net profit per hour:
\[
30 \times H = 90
\]
- Solving for \(H\):
\[
H = \frac{90}{30} = 3 \text{ hours}
\]
3. **Calculate total expenses and receipts after 3 hours:**
- Total receipts after 3 hours:
\[
\text{Total receipts} = \text{Average hourly receipts} \times H = 44 \times 3 = 132 \text{ dollars}
\]
- Total expenses after 3 hours:
\[
\text{Total expenses} = \text{Average hourly operating costs} \times H = 14 \times 3 = 42 \text{ dollars}
\]
4. **Total expenses and receipts will both equal:**
- Since the total profit is $90, the total receipts will equal the total expenses plus the profit:
\[
\text{Total receipts} = \text{Total expenses} + 90
\]
But since we calculated the different totals:
- Total receipts = $132
- Total expenses = that plus the original operating costs which will be $132 - $90 = $42.
In conclusion, the total expenses and receipts will both total $132 after 3 hours.
**Final Answer:**
The bakery's expenses and receipts will both total $132 after 3 hours.