Question

On a certain day, a bakery produced a batch of rolls at a total production cost of $300. On that day, $\frac{4}{5}$ of the rolls in the batch were sold, each at a price that was 50 percent 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 percent less than the price of the day before. What was the bakery's profit on this batch of rolls?
A. $ 150
B. $ 144
C. $ 132
D. $ 108
E. $ 90

Answer 1

Answer:

The profit of the bakery for this batch of rolls is C. $ 132

Step-by-step explanation:

You know the following this about the problem:

• xy=300 is the total cost of the production of the rolls, where x is the cost of the rolls and y is the number of rolls.
• Day 1 the bakery sold 4/5 of the rolls at 1.50 its value.
• Day 2 the bakery sold 1/5 of the rolls ar 0.8 of the price of Day 1.

$Day1=1.50x\frac{4}{5}y=\frac{3}{2}x\frac{4}{5}y=\frac{6}{5}xy\\Day2=0.8\frac{3}{2}x\frac{1}{5}y=\frac{4}{5}\frac{3}{2}x\frac{1}{5}y=\frac{6}{25}xy$

The total gain of the sales is:

Day 1 + Day 2

$Day1+Day2=\frac{6}{5}xy+\frac{6}{25}xy=\frac{36}{25}xy$

and you know that xy =300, then the total gain is:

$gain=\frac{36}{25}(300)=432$

And the profit is the total gain less the total cost:

Profit = 432-300=132