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 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

Answer 1

$108

Explanation:

Let number of rolls produced =
`x`

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 = $
`(300)/(x)`

`(4)/(5)` of the rolls were sold at a price 50% higher than the average production cost per roll.

i.e.

Money earned by selling
`(4)/(5)` of the rolls:

`(4)/(5)x * (300)/(x)* (150)/(100)\\\Rightarrow \$360`

Money earned by selling the remaining the remaining rolls:

`(1)/(5)x* (300)/(x)* (80)/(100)\\\Rightarrow \$48`

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