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Judy bought a quantity of pens in packages of 5 for $0.80 per package

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Judy bought a quantity of pens in packages of 5 for $0.80 per package. She sold all of the pens in packages of 3 for $0.60 per package. If Judy's profit from the pens was $8.00, how many pens did she buy and sell?

A. 40

B. 80

C. 100

D. 200

E. 400
[Reveal] Spoiler: OA

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Re: Judy bought a quantity of pens in packages of 5 for $0.80 per package [#permalink]

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carcass wrote:
Judy bought a quantity of pens in packages of 5 for $0.80 per package. She sold all of the pens in packages of 3 for $0.60 per package. If Judy's profit from the pens was $8.00, how many pens did she buy and sell?

A. 40

B. 80

C. 100

D. 200

E. 400


It should be D.

Cost price per pen = $0.80 / 5 = $0.16 or 16 cents.
Sale price per pen = $0.60 / 3 = $0.20 or 20 cents.
Profit per pen = 0.20 - 0.16 = $0.04 or 4 cents.

Profit = Profit per pen x number of pens

number of pens = Profit/profit per pen = 8/0.04 = 200
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Judy bought a quantity of pens in packages of 5 for $0.80 per package [#permalink]

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New post 23 Jul 2017, 16:59
carcass wrote:
Judy bought a quantity of pens in packages of 5 for $0.80 per package. She sold all of the pens in packages of 3 for $0.60 per package. If Judy's profit from the pens was $8.00, how many pens did she buy and sell?

A. 40

B. 80

C. 100

D. 200

E. 400

carcass, you are a master of crafty language, and this one takes the prize.

The trap is in the second sentence: "She sold all of the pens in packages of 3 for $0.60 per package."

That sentence does not mean that all the pens she sold were in packages of 3. In fact, coupled with the implication of answers that are not multiples of 15, the sentence means just the opposite; it means "not all the pens sold were in boxes of 3."

A quantity that can be divided evenly into 5 per package and into 3 per package must be divisible by 15. None of the answer choices offers that possibility.

So the pens Judy sold were not all in packages of 3.

We have total profit. To get the number of pens, we need Judy's cost per pen and her sell price per pen.

A package of five pens cost Judy 80 cents. \(\frac{80}{5}\) = each pen cost 16 cents.

A package of three pens sold for 60 cents.\(\frac{60}{3}\) = each pen sold for 20 cents.

Profit per pen is 20 - 16 = 4 cents' profit per pen.

Total profit = (profit per pen) * (number N of pens sold)

$8.00 = ($0.04)N

\(\frac{$8.00}{($0.04)}\) = 200

Number of pens sold: 200

Answer D

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Re: Judy bought a quantity of pens in packages of 5 for $0.80 per package [#permalink]

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New post 23 Jul 2017, 17:17
carcass wrote:
Judy bought a quantity of pens in packages of 5 for $0.80 per package. She sold all of the pens in packages of 3 for $0.60 per package. If Judy's profit from the pens was $8.00, how many pens did she buy and sell?

A. 40
B. 80
C. 100
D. 200
E. 400

I. Cost per pen = 0.80/5 = (4/5)/5 = (4/5)*(1/5) = 4/25 = 16/100 = 0.16;
II. Revenue per pen = 0.60/3 = 6/30 = 1/5 = 0.20;
III. Profit per pen = Revenue per pen - Cost per pen = 0.20 - 0.16 = 0.04;
IV. Total profit = profit per pen * quantity of pens: (8) = (0.04) * quantity, quantity = 8/0.04 = 800/4 = 200.

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Re: Judy bought a quantity of pens in packages of 5 for $0.80 per package [#permalink]

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New post 24 Jul 2017, 00:48
carcass wrote:
Judy bought a quantity of pens in packages of 5 for $0.80 per package. She sold all of the pens in packages of 3 for $0.60 per package. If Judy's profit from the pens was $8.00, how many pens did she buy and sell?

A. 40

B. 80

C. 100

D. 200

E. 400


Cost price: packages of 5 for $0.80 per package = $0.80/5 = $0.16 per pen.
Selling price: packages of 3 for $0.60 per package = $0.60/3 = $0.2 per pen.

Profit = ¢4 per pen.
Total profit = ¢800.
The number of pens = 800/4 = 200.

Answer: D.
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Re: Judy bought a quantity of pens in packages of 5 for $0.80 per package [#permalink]

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New post 24 Jul 2017, 09:21
\(\frac{x}{5} * (0.8) - \frac{x}{3}*(0.6)\) = 8

\(\frac{2.4x - 3x}{15} = 8\)

x=200
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Re: Judy bought a quantity of pens in packages of 5 for $0.80 per package [#permalink]

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New post 24 Jul 2017, 10:14
carcass wrote:
Judy bought a quantity of pens in packages of 5 for $0.80 per package. She sold all of the pens in packages of 3 for $0.60 per package. If Judy's profit from the pens was $8.00, how many pens did she buy and sell?

A. 40

B. 80

C. 100

D. 200

E. 400


CP of a pen = \(\frac{80}{5} = 16\)

SP of a pen = \(\frac{60}{3} = 20\)

Profit = \(20-16 = 4\), per pen.

Total profit = \(800\), so number of pens = \(\frac{800}{4} = 200\). Ans - D.
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Re: Judy bought a quantity of pens in packages of 5 for $0.80 per package [#permalink]

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New post 26 Jul 2017, 16:37
carcass wrote:
Judy bought a quantity of pens in packages of 5 for $0.80 per package. She sold all of the pens in packages of 3 for $0.60 per package. If Judy's profit from the pens was $8.00, how many pens did she buy and sell?

A. 40

B. 80

C. 100

D. 200

E. 400


We can let x = the number of pens she bought and sold. Since she bought the pens in packages of 5, she bought x/5 packages. Similarly, since she sold the pens in packages of 3, she sold x/3 packages. She bought the packages at $0.80 each and sold them at $0.60 each, and her profit is $8.00; thus, we can create the following equation:

0.60(x/3) - 0.80(x/5) = 8.00

60(x/3) - 80(x/5) = 800

20x - 16x = 800

4x = 800

x = 200

Answer: D
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Judy bought a quantity of pens in packages of 5 for $0.80 per package [#permalink]

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New post 05 Sep 2017, 08:35
carcass wrote:
Judy bought a quantity of pens in packages of 5 for $0.80 per package. She sold all of the pens in packages of 3 for $0.60 per package. If Judy's profit from the pens was $8.00, how many pens did she buy and sell?

A. 40

B. 80

C. 100

D. 200

E. 400



Profit = revenue - cost; Revenue = Sales price x quantity; cost = buy price x quantity
profit = profit per individual pen x total number of pens

Saleprice/pen = 0.60/3 = .20 cents per pen
Buyprice/pen =0.80/5 = .16 cents per pen on the buy
profit per pen = .20 - .16 = .04 cents profit per pen

Profit = profit per pen x number of pens bought and sold
8.00 = .04 x N
200 = number of pens bought and sold

bottom line with this one is to start out finding the cost of individual pen and the sale of individual pen. once you find the individual profit, set your variable, and divide from the total profit given.

I got this one right, but idk, something weird with the way it is worded threw me off balance for a bit.

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Judy bought a quantity of pens in packages of 5 for $0.80 per package   [#permalink] 05 Sep 2017, 08:35
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