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How many nails did Rudy buy if he purchased them at a price of $0.25

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Nums99
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How many nails did Rudy buy if he purchased them at a price of $0.25 [#permalink] New post   Updated on: 12 Jan 2019, 03:25
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How many nails did Rudy buy if he purchased them at a price of $0.25 per four nails, sold them at $0.22 per three nails, and made a profit of $2.60?

A. 300
B. 240
C. 180
D. 160
E. 120
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B

Originally posted by Nums99 on 12 Jan 2019, 01:42.
Last edited by Bunuel on 12 Jan 2019, 03:25, edited 1 time in total.
Renamed the topic, edited the question, moved to PS and added the OA.
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Re: How many nails did Rudy buy if he purchased them at a price of $0.25 [#permalink] New post   12 Jan 2019, 02:12
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Hi there,

Here's the solution.

Let the number of nails Rudy purchased be x.

Rudy purchased nails at a price of $0.25 per four nails. So, Cost Price of 4 nails = $0.25
Cost Price of 1 nail = = $0.25/4
Cost price of x nails = ($0.25/4)x

Also given that Rudy sold nails at $0.22 per three nails. So, Selling Price of 3 nails = $0.22
Selling Price of 1 nail = = $0.22/3
Selling price of x nails = ($0.22/3)x


Also, Rudy made a profit of $2.60.
Profit = Selling Price - Cost Price
$2.60 = ($0.22/3)x - ($0.25/4)x = x(0.88 - 0.75)/12
$2.60 = x(0.13)/12
x = 240
Hence, the the number of nails Rudy purchased is 240.

Therefore, the Correct Answer is Option B. 240
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Re: How many nails did Rudy buy if he purchased them at a price of $0.25 [#permalink] New post   16 Jan 2019, 02:57
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Nums99 wrote:
How many nails did Rudy buy if he purchased them at a price of $0.25 per four nails, sold them at $0.22 per three nails, and made a profit of $2.60?

A. 300
B. 240
C. 180
D. 160
E. 120


Profit = Sales - Cost

\(2.6 = \frac{0.22}{3}n - \frac{0.25}{4}n = \frac{0.88n}{12} - \frac{0.75n}{12}\)
\(\frac{13}{5} = \frac{0.13n}{12} = \frac{13n}{1200}\)
\(n = \frac{13*1200}{13*5} = 240\)

B
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Re: How many nails did Rudy buy if he purchased them at a price of $0.25 [#permalink] New post   16 Jan 2019, 08:15
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As we are dealing with two numbers 3 & 4 .... lets take the LCM of them i.e.,12 .
Cost price for 12 nails = $0.25*12/4=$0.75 & Selling price for 12 nails = $0.22*12/3=$0.88
Profit made per 12 nails = $0.88 - $0.75 = $0.13
So total '12 units' sold = $2.60/$0.13 =20
Total nails sold = 20*12 = 240 .... Thus Ans would be option B.
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Re: How many nails did Rudy buy if he purchased them at a price of $0.25 [#permalink] New post   25 Feb 2019, 09:26
Nums99 wrote:
How many nails did Rudy buy if he purchased them at a price of $0.25 per four nails, sold them at $0.22 per three nails, and made a profit of $2.60?

A. 300
B. 240
C. 180
D. 160
E. 120


LCM approach is good in such questions:-

Rudy purchased nails at a price of $0.25 per four nails, or $0.75 per 12 nails

sold them at $0.22 per three nails, or $0.88 per 12 nails

and made a profit of $2.60 (total) or $(0.88-0.75) = $ 0.13 per 12 nails

(2.60 * 12)/0.13 = 240 nails (Ans)
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How many nails did Rudy buy if he purchased them at a price of $0.25 [#permalink] New post   28 Feb 2019, 11:09
Nums99 wrote:
How many nails did Rudy buy if he purchased them at a price of $0.25 per four nails, sold them at $0.22 per three nails, and made a profit of $2.60?

A. 300
B. 240
C. 180
D. 160
E. 120


Cost Price of \(4\) nails \(= $ 0.25\)

Cost Price of \(3\) nails \(= \frac{0.25*3}{4} = $ 0.1875\)

Selling Price of \(3\) nails \(= $0.22\)

Profit on \(3\) nails \(= 0.22 - 0.1875 = $ 0.0325\)

Let \("x"\) be total number of nails to make profit of \($ 2.60\).

\(\frac{0.0325}{3} = \frac{2.60}{x}\)

\(0.0325*x =3*2.60\)

\(x = \frac{3*2.60}{0.0325} = 240\)

Answer B
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Re: How many nails did Rudy buy if he purchased them at a price of $0.25 [#permalink] New post   02 Mar 2019, 10:08
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Nums99 wrote:
How many nails did Rudy buy if he purchased them at a price of $0.25 per four nails, sold them at $0.22 per three nails, and made a profit of $2.60?

A. 300
B. 240
C. 180
D. 160
E. 120


We can let n = the number of nails and create the equation:

(0.22/3)n - (0.25/4)n = 2.6

Multiplying by 12, we have:

0.22 x 4n - 0.25 x 3n = 31.2

0.88n - 0.75n = 31.2

0.13n = 31.2

n = 240

Answer: B
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Re: How many nails did Rudy buy if he purchased them at a price of $0.25 [#permalink] New post   19 Jul 2020, 06:01
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Re: How many nails did Rudy buy if he purchased them at a price of $0.25 [#permalink]
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