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A small business invests $9,900 in equipment to produce a

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petercao
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A small business invests $9,900 in equipment to produce a [#permalink] New post   Updated on: 21 Jul 2015, 02:20
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A small business invests $9,900 in equipment to produce a product. Each unit of the product costs $0.65 to produce and is sold for $1.20. How many units of the product must be sold before the revenue received equals the total expense of production, including the initial investment in equipment?

A. 12,000
B. 14,500
C. 15,230
D. 18,000
E. 20,000
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D

Originally posted by petercao on 08 Nov 2008, 21:16.
Last edited by Bunuel on 21 Jul 2015, 02:20, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: A small business invests $9,900 in equipment to produce a [#permalink] New post   20 Jul 2015, 13:32
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A small business invests $9,900 in equipment to produce a product. Each unit of the product costs $0.65 to produce and is sold for $1.20. How many units of the product must be sold before the revenue received equals the total expense of production, including the initial investment in equipment?

A. 12,000
B. 14,500
C. 15,230
D. 18,000
E. 20,000



If we ask the question a different way, that answer is much easier to see. The company makes $0.55 ($1.20 less the $0.65) on each product. so how many of these products will need to be made to cover the initial $9,900 equipment cost. 9,900/0.55 will give us the answer. 9,900/0.55 is 18,000 ==> the correct answer is D.
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Re: A small business invests $9,900 in equipment to produce a [#permalink] New post   08 May 2019, 08:24
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petercao wrote:
A small business invests $9,900 in equipment to produce a product. Each unit of the product costs $0.65 to produce and is sold for $1.20. How many units of the product must be sold before the revenue received equals the total expense of production, including the initial investment in equipment?

A. 12,000
B. 14,500
C. 15,230
D. 18,000
E. 20,000


Let x = the number of units produced AND sold

TOTAL COST
If each unit of the product costs $0.65 to produce, then it costs 0.65x dollars to produce x units
We must also add the $9,900 investment in equipment
So, TOTAL COST = 0.65x + 9900

TOTAL REVENUE
If each unit sells for $1.20 to produce, then selling x units results in TOTAL SALES of 1.2x dollars

We want: TOTAL REVENUE = TOTAL COST
In other words: 1.2x = 0.65x + 9900
Subtract 0.65x from both sides: 0.55x = 9900
Solve: x = 9900/0.55

PRO TIP: We know that 9900/0.5 = 19,800
Since 0.55 is a bit bigger than 0.5, we know that 9900/0.55 = a little bit LESS THAN 19,800

Answer: D

Cheers,
Brent
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Re: A small business invests $9,900 in equipment to produce a [#permalink] New post   08 Nov 2008, 21:34
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petercao wrote:
A small business invests $9,900 in equipment to produce a product. Each unit of the product costs $0.65 to produce and is sold for $1.20. How many units of the product must be sold before the revenue received equals the total expense of production, including the initial investment in equipment?

A. 12,000
B. 14,500
C. 15,230
D. 18,000
E. 20,000


the total expense of production is 9,900+0.65x
and the revenue is 1.20x

so x=18,000
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Re: A small business invests $9,900 in equipment to produce a [#permalink] New post   08 Nov 2008, 21:35
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x is the number of units

Total product cost = total expense = 0.65x
Total product sale prices: 1.2x

Revenue receive = 1.2x - 9,900

1.2x - 9,900 = 0.65 <=> x = 18,000 (D)
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Re: A small business invests $9,900 in equipment to produce a [#permalink] New post   10 May 2019, 17:34
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petercao wrote:
A small business invests $9,900 in equipment to produce a product. Each unit of the product costs $0.65 to produce and is sold for $1.20. How many units of the product must be sold before the revenue received equals the total expense of production, including the initial investment in equipment?

A. 12,000
B. 14,500
C. 15,230
D. 18,000
E. 20,000



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

1.2n = 9,900 + 0.65n

0.55n = 9,900

n = 18,000

Answer: D
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Re: A small business invests $9,900 in equipment to produce a [#permalink] New post   11 May 2019, 04:54
petercao wrote:
A small business invests $9,900 in equipment to produce a product. Each unit of the product costs $0.65 to produce and is sold for $1.20. How many units of the product must be sold before the revenue received equals the total expense of production, including the initial investment in equipment?

A. 12,000
B. 14,500
C. 15,230
D. 18,000
E. 20,000


Proft per unit =(1.2-0.65)=0.55

9900/0.55=18000 more units of product must be sold to cover the production cost.

Answer is D

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Re: A small business invests $9,900 in equipment to produce a [#permalink] New post   29 Dec 2020, 03:17
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petercao wrote:
A small business invests $9,900 in equipment to produce a product. Each unit of the product costs $0.65 to produce and is sold for $1.20. How many units of the product must be sold before the revenue received equals the total expense of production, including the initial investment in equipment?

A. 12,000
B. 14,500
C. 15,230
D. 18,000
E. 20,000


There is a good formula (equation) for this kind of PS.

Sales = Variable cost+Fixed cost + Profit. [Production cost is the variable cost and the Profit will be "0" here, as the question stem asked for a quantity where total revenue will be equal to total cost]

Let, the desired quantity is \(Q\)

\(1.20Q=0.65Q+9,900+0\)

\(=0.55Q=9,900\)

\(Q=\frac{9,900*100}{55}=18,000\)

The answer is \(D\)
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Re: A small business invests $9,900 in equipment to produce a [#permalink] New post   07 May 2021, 21:56
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petercao wrote:
A small business invests $9,900 in equipment to produce a product. Each unit of the product costs $0.65 to produce and is sold for $1.20. How many units of the product must be sold before the revenue received equals the total expense of production, including the initial investment in equipment?

A. 12,000
B. 14,500
C. 15,230
D. 18,000
E. 20,000


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Re: A small business invests $9,900 in equipment to produce a [#permalink] New post   11 Sep 2021, 13:39
ScottTargetTestPrep wrote:
petercao wrote:
A small business invests $9,900 in equipment to produce a product. Each unit of the product costs $0.65 to produce and is sold for $1.20. How many units of the product must be sold before the revenue received equals the total expense of production, including the initial investment in equipment?

A. 12,000
B. 14,500
C. 15,230
D. 18,000
E. 20,000



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

1.2n = 9,900 + 0.65n

0.55n = 9,900

n = 18,000

Answer: D


I thought because the uestion says "before", that we need to find the value before the break even, which is 18,000, so I chose choice C.
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Re: A small business invests $9,900 in equipment to produce a [#permalink] New post   25 Jul 2022, 05:06
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Re: A small business invests $9,900 in equipment to produce a [#permalink] New post   25 Jul 2023, 06:39
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