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On a certain day, a bakery produced a batch of rolls at a total produc

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On a certain day, a bakery produced a batch of rolls at a total produc  [#permalink]

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New post 25 Jul 2017, 11:43
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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, \(\frac{4}{5}\) 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

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On a certain day, a bakery produced a batch of rolls at a total produc  [#permalink]

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New post 23 Aug 2017, 21:16
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My approach:

Let x is the number of rolls made. Average cost is 300/x.

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,
so first day revenue = \(\frac{4x}{5}\) x \(\frac{300}{x}\) x 150%

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,
so second day revenue = \(\frac{x}{5}\) x \(\frac{300}{x}\) x 150% x 80%

Total Revenue = \(\frac{4x}{5}\) x \(\frac{300}{x}\) x 150% + \(\frac{x}{5}\) x \(\frac{300}{x}\) x 150% x 80%
= 432 (x will be canceled out)

Cost = 300, so Profit = 432-300 = 132
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On a certain day, a bakery produced a batch of rolls at a total produc  [#permalink]

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New post 25 Jul 2017, 14:16
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carcass wrote:
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

Method I - assign a value to number of rolls total

Because all the rolls are sold, and because they are all sold at equal prices on their respective days, we can use any number of rolls we want to calculate
Profit as (Total Revenue - Total Cost).

The profit is the same for 300 rolls that cost $300 as it is for 30 rolls that cost $300.

Let # of rolls = 30
Cost per roll = $10

Day 1: \(\frac{4}{5}\) of 30, or 24 rolls, are sold at 50 percent above cost -->
Day 1, PRICE: 50% above cost is (1.5 * $10) = $15 each

Day 1, Total Revenue: (24 * $15) = $360

Day 2: remaining 6 rolls are sold at 80 percent of Day 1's price (of $15) -->
Day 2's price is (.8 * $15)= $12 each

Day 2, Total Revenue: (6 * $12) = $72

Total Revenue for both days: ($360 + $72) = $432

(TR - TC) = PROFIT
PROFIT = ($432 - $300) = $132

Answer C

Method II - Algebra

\(xy = 300\) = Total cost, where \(x\) is unit cost of rolls and \(y\) is # of rolls

Day 1 = \(\frac{4}{5}y * \frac{3}{2}x = \frac{6}{5}xy\)

Day 2 = \(\frac{1}{5}y * (\frac{4}{5}*\frac{3}{2})x\)

\(= (\frac{1}{5}y*\frac{12}{10}x)=\frac{12}{50}xy=\frac{6}{25}xy\)

Day 1 + Day 2: \((\frac{6}{5}xy + \frac{6}{25}xy)= \frac{36}{25}xy\)

\(xy = 300\), so
Total revenue = \((\frac{36}{25})($300) = $432\)

Total cost = \($300\)
Profit = (TR - TC)
Profit = \($132\)

Answer C
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Re: On a certain day, a bakery produced a batch of rolls at a total produc  [#permalink]

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New post 09 Aug 2017, 13:32
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carcass wrote:
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


We can let the production cost per roll = x and the total number of rolls = t.

On the same day the rolls were made, we are given that (4/5)t rolls were sold at 1.5x each. So the revenue was (1.5x)(4/5)t = 1.2xt

On the following day, we are given that (1/5)t of the rolls were sold for 0.8(1.5x) = 1.2x each. So the revenue was 1.2x(1/5)t = 0.24xt.

Since the production cost was 300:

300 = xt

So,

Profit = (1.2xt + 0.24xt) - xt

profit = (1.44xt) - xt

profit = 1.44(300) - 300 = 132 dollars.

Answer: C
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On a certain day, a bakery produced a batch of rolls at a total produc  [#permalink]

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New post 01 Sep 2017, 06:13
Let no. of rolls = n
production cost of each roll =p

Given total production cost = n*p =300

Now 1st day : 4/5 no. of rolls were sold at 50% more than production price:
so selling price = (1+50/100)p = 1.5p

so revenue on 1st day = (4/5 *n) *(1.5p) = 1.2 np

now second day: remaining rolls ie 1/5th of rolls sold at 20% less than previous day price :
so selling price = (1-20/100)(1.5p) = 0.8 *1.5p

so revenue on 2nd day = (1/5 *n) *(0.8 * 1.5p) = 0.24 np

Total revenue = 1.2np +0.24np = 1.44np
as np=300
Total revenue = 1.44* 300 = 432

Profit = Revenue - production cost = 432-300 = 132

Answer : C
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Re: On a certain day, a bakery produced a batch of rolls at a total produc  [#permalink]

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New post 08 Sep 2017, 20:37
Can anyone tell me what is wrong with my calculation? carcass

Assume batch of rolls =5
Cost per roll = $300/5= $60

First day sales : 4/5*5*$60*1.5 = $360
Second day sales : 1/5*5*$60*0.8 = $48
Total sales = $408
Profit = $408-$300 = $108
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Re: On a certain day, a bakery produced a batch of rolls at a total produc  [#permalink]

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New post 08 Sep 2017, 22:03
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chid2 wrote:
Can anyone tell me what is wrong with my calculation? carcass

Assume batch of rolls =5
Cost per roll = $300/5= $60

First day sales : 4/5*5*$60*1.5 = $360
Second day sales : 1/5*5*$60*0.8 = $48
Total sales = $408
Profit = $408-$300 = $108


Hi,

The question stem said that "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"
So your calculation for second day sale should be 1/5*5*$60*1.5*0.8 = 72.
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Re: On a certain day, a bakery produced a batch of rolls at a total produc  [#permalink]

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New post 12 Sep 2017, 08:20
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carcass wrote:
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





Since they never give you total amount of rolls produced, just make it 100 rolls, because 100 is an easy number to work with.

Total cost = $300
Total rolls produced = 100
$3.00 per roll
50% of $3.00 is $4.50
4/5 of 100 is 80
80 x 4.50 = $360.00
20% of 4.50 = $.90
4.50 - .90 = $3.60
3.60 x 20 = $72.00
$360.00 + $72.00 = $432.00
$432.00(revenue) - $300.00(cost) = $132.00 (Profit)

Ans is (C)
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On a certain day, a bakery produced a batch of rolls at a total produc  [#permalink]

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New post 22 Nov 2017, 09:05
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I cant's understand why we can't just simply find the cost of goods sold at the first day = 240 (4/5=300)
Then add a margin of 1.5, 240*1.5= 360 (sales) and get profit of the 1st day 360-240 = 120
Then why can't we simply apply 0.8 discount (20% off) to the gross margin for the 1st day of 1.5*0.8 and get 1.2
Applying to 1.2 to 60 (cost of goods sold of the 2nd day, which is found as 300*1/5) = 72 (sales)
72-60 = 12 and 120 + 12 = 132
Why do we need to imagine a number of units sold or write equations?
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Re: On a certain day, a bakery produced a batch of rolls at a total produc  [#permalink]

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New post 11 Sep 2018, 21:10
suppose there are \(100\) roles in a batch
Average price per role is\(=300/100=3\)
as \(4/5\) of \(100\) roles \(= 80 roles\)
\(80\) roles sold at price \(1.5*3=4.5\)
total revenue out of \(80\) roles\(=80*4.5=360\)

Now, remaining \(20\) roles sold at price \(20%\) less than previous day price \((4.5)\)
So price per role for day 2 is \(= 0.8*4.5=3.6\)
Revenue out of \(20\) roles on day 2 \(= 20*3.6=72\)

So total revenue of \(100\) roles \(= 360+72=432\)
\(Profit=Revenue-Cost=432-300=132\)

Answer C
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Re: On a certain day, a bakery produced a batch of rolls at a total produc &nbs [#permalink] 11 Sep 2018, 21:10
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