Question

On a certain day, a bakery produced a batch of rolls at a total production cost of $300. On that day, (4/5) of the rolls in the batch were sold, each at a price that was 50% greater than the average (arithmetic mean) production cost per roll. The remaining rolls in the batch were sold the next day, each at a price that was 20% less than the price of the day before. What was the bakery's profit on this batch of rolls?

Hint:

To calculate profit, subtract the total cost from the total revenue. When items are sold at different prices, calculate the revenue for each price and add them up.

Answer 1

Step 1: Calculate the average production cost per roll.
Let \( n \) be the number of rolls produced. The total production cost is $300, so the average production cost per roll is:
\[ \text{Average cost per roll} = \frac{300}{n} \] Step 2: Calculate the price at which the rolls were sold on the first day.
On the first day, \( \frac{4}{5} \) of the rolls were sold at a price 50% greater than the average cost per roll. The price per roll on the first day is:
\[ \text{Price per roll (first day)} = 1.5 \times \frac{300}{n} \] Step 3: Calculate the revenue from the rolls sold on the first day.
The revenue from \( \frac{4}{5}n \) rolls sold on the first day is:
\[ \text{Revenue (first day)} = \frac{4}{5}n \times 1.5 \times \frac{300}{n} = 1.5 \times 300 = 450 \] Step 4: Calculate the price at which the rolls were sold on the second day.
On the second day, the remaining \( \frac{1}{5}n \) rolls were sold at a price 20% less than the price of the first day. The price per roll on the second day is:
\[ \text{Price per roll (second day)} = 0.8 \times 1.5 \times \frac{300}{n} = 1.2 \times \frac{300}{n} \] Step 5: Calculate the revenue from the rolls sold on the second day.
The revenue from the remaining \( \frac{1}{5}n \) rolls is:
\[ \text{Revenue (second day)} = \frac{1}{5}n \times 1.2 \times \frac{300}{n} = 1.2 \times 60 = 72 \] Step 6: Calculate the total revenue.
The total revenue from both days is:
\[ \text{Total revenue} = 450 + 72 = 522 \] Step 7: Calculate the profit.
The total cost of producing \( n \) rolls is $300, so the profit is:
\[ \text{Profit} = \text{Total revenue} - \text{Total cost} = 522 - 300 = 222 \] Step 8: Conclusion.
The bakery's profit on this batch of rolls is $222.