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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 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

Sagot :

isyllus

Answer:

$108

Step-by-step explanation:

Let number of rolls produced = [tex]x[/tex]

Total production cost = $300

Average production cost can be found by dividing the total production cost with the number of rolls produced.

Average production cost per roll = $[tex]\frac{300}{x}[/tex]

[tex]\frac{4}{5}[/tex] of the rolls were sold at a price 50% higher than the average production cost per roll.

i.e.

Money earned by selling [tex]\frac{4}{5}[/tex] of the rolls:

[tex]\dfrac{4}{5}x \times \dfrac{300}{x}\times \dfrac{150}{100}\\\Rightarrow \$360[/tex]

Money earned by selling the remaining the remaining rolls:

[tex]\dfrac{1}{5}x\times \dfrac{300}{x}\times \dfrac{80}{100}\\\Rightarrow \$48[/tex]

Total money earned by selling all the rolls = $360 + $48 = $408

Total profit can be calculated by subtracting the total production cost from the total money earned.

Total profit = $408 - $300 = $108

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