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A computer store has fixed monthly operating costs of 5,000 dollars.

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A computer store has fixed monthly operating costs of 5,000 dollars.  [#permalink]

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New post 18 Jul 2018, 21:09
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A computer store has fixed monthly operating costs of 5,000 dollars. The store buys each computer for 600 dollars and sells each computer for 900 dollars. What is the least number of computers the store must sell each month to cover the fixed operating costs?

A. 14
B. 15
C. 16
D. 17
E. 18

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Re: A computer store has fixed monthly operating costs of 5,000 dollars.  [#permalink]

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New post 18 Jul 2018, 21:17
C.P = 600
S.P = 900
PROFIT = S.P - C.P = 300
OPERATING COSTS = 5000
LEAST NUMBER OF COMPUTERS TO BE SOLD TO COVER THE OPERATING COSTS = 500O/PROFIT
= 5000/300
~ 17

ANSWER : D

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A computer store has fixed monthly operating costs of 5,000 dollars.  [#permalink]

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New post 19 Jul 2018, 01:09
Bunuel wrote:
A computer store has fixed monthly operating costs of 5,000 dollars. The store buys each computer for 600 dollars and sells each computer for 900 dollars. What is the least number of computers the store must sell each month to cover the fixed operating costs?

A. 14
B. 15
C. 16
D. 17
E. 18


Let x be the computers sold.

The profit made by the computer store on a computer is \($300($900 - $600)\)
The profit made when x computers are sold is 300x. For this profit to be more
than the fixed monthly operating costs

\(300x > 5000\) -> \(x > \frac{5000}{300}\) or \(16.67\)

Therefore, the least number of computers the store must sell to cover the fixed costs is 17(Option D)
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Re: A computer store has fixed monthly operating costs of 5,000 dollars.  [#permalink]

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New post 19 Jul 2018, 01:25
+1 for D.

Cost Price = 600 $
Selling Price = 900 $

Profit = 900 - 600 = 300 $

Total number of computer to be sold;
= 5000 / 300
= 16.66
= 17 (approx.)

Hence, D.
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Re: A computer store has fixed monthly operating costs of 5,000 dollars.  [#permalink]

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New post 19 Jul 2018, 05:35

Solution



Given:

    • Computer store has fixed monthly operating costs of 5,000 dollars
    • The store buys each computer for 600 dollars and sells each computer for 900 dollars.

To find:

    • The least number of computers the store must sell each month to cover the fixed operating costs

Approach and Working:

Least number of computers will be the number of sold by him such that he makes no loss no profit i.e. selling price= cost price + operational cost.

Let he buys and sells ‘n’ computers.
    • n* 900= n*600+5000
    • n*300= 5000
    • n= 50/3= 16.666..

However, the number of computers sold can never be a decimal.
Hence, the minimum number of computers he should sell= 17.

Hence, the correct answer is option D.

Answer: D
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Re: A computer store has fixed monthly operating costs of 5,000 dollars.  [#permalink]

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New post 22 Jul 2018, 18:32
Bunuel wrote:
A computer store has fixed monthly operating costs of 5,000 dollars. The store buys each computer for 600 dollars and sells each computer for 900 dollars. What is the least number of computers the store must sell each month to cover the fixed operating costs?

A. 14
B. 15
C. 16
D. 17
E. 18


We can create the equation:

900x = 5,000 + 600x

300x = 5,000

3x = 50

x = 50/3 = 16 ⅔, so 17 computers must be sold.

Alternate Solution:

We see that each computer sold generates 300 dollars of profit. This means that the store must sell 5,000/300, or 16 ⅔ computers to cover the fixed operating costs. We thus round up to 17 computers..

Answer: D
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Re: A computer store has fixed monthly operating costs of 5,000 dollars.   [#permalink] 22 Jul 2018, 18:32
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