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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
A. 12,000
B. 14,500
C. 15,230
D. 18,000
E. 20,000
Posts: 108
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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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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Posts: 6,727
petercao
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
General Discussion
petercao
the total expense of production is 9,900+0.65x
and the revenue is 1.20x
so x=18,000
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)
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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Expert reply
Posts: 22,738
petercao
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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Posts: 36
petercao
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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petercao
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 \(D\)
petercao
Answer: Option D
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Posts: 11
ScottTargetTestPrep
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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Expert reply
Video solution from Quant Reasoning:
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Posts: 7
Investmwnt is $9900
cost=$0.65
SP=$1.2
The question is asking product must be sold [before Sales=cost
Therefore Iassumeit should be sales shoukd be less than the below equation which is calculated
no of units=x
1.2x=.65x+9900
after solving we get 18000 units
hence it should be less than 18000 becoz its saying before in the question stem
plz explain Bunuel
cost=$0.65
SP=$1.2
The question is asking product must be sold [before Sales=cost
Therefore Iassumeit should be sales shoukd be less than the below equation which is calculated
no of units=x
1.2x=.65x+9900
after solving we get 18000 units
hence it should be less than 18000 becoz its saying before in the question stem
plz explain Bunuel
atquereiciendis
Your confusion is treating “before” as “earlier in time.” In this problem, “before” means “up to the point where” (the threshold). You are being asked for the unit count at that threshold, not a time earlier and not “anything less than it.” Selling fewer units means you have not yet reached the point where revenue equals total expense.
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