A personal chef charges $140 per four-person meal; her monthly expenses are $2800. How many four-person meals must he sell in order to make a profit of at least $4000?
The correct answer and explanation is:
To find the number of four-person meals the chef must sell to make a profit of at least $4000, let’s break down the problem step by step:
1. Calculate the revenue per meal:
The chef charges $140 per four-person meal. Therefore, for each meal sold, the chef earns $140 in revenue.
2. Calculate the total amount the chef needs to earn:
The chef needs to make a profit of at least $4000. However, the chef also has monthly expenses of $2800. So, the total amount of money the chef needs to cover both expenses and make the desired profit is: Total required revenue=Expenses+Desired profit\text{Total required revenue} = \text{Expenses} + \text{Desired profit} Total required revenue=2800+4000=6800\text{Total required revenue} = 2800 + 4000 = 6800
3. Set up the equation to find the number of meals:
Let the number of meals the chef needs to sell be denoted as xx. The total revenue from selling xx meals is: Revenue from x meals=140x\text{Revenue from } x \text{ meals} = 140x
To make at least $6800 in revenue, we set up the following inequality: 140x≥6800140x \geq 6800
4. Solve for xx:
Now, solve for xx to find the number of meals the chef needs to sell: x≥6800140=48.57x \geq \frac{6800}{140} = 48.57
Since the chef can’t sell a fraction of a meal, round up to the next whole number. Therefore, the chef needs to sell at least 49 meals to make a profit of at least $4000.
Conclusion:
The chef must sell 49 four-person meals to make a profit of at least $4000, covering both expenses and the desired profit margin.