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Question 79925: Hi, I need help in figuring out this problem. I can get some of it, I think I know how to get how many units in the case but not really sure.
The owner of a hobby store bought a case of 9-volt batteries for $26.00. He marked the price up such that his profit was $1.74 per battery. After selling 13 batteries, the store owner had recovered his cost. How many 9-volt batteries are in a case?
thanks for the help
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! There are a couple of ways of looking at this problem.
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First ... by selling 13 batteries the owner recovers the $26 that the case cost him.
Let's find the price (P) he is charging per battery. That price times 13 batteries must
equal $26. In equation form this becomes:
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P * 13 = $26
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Divide both sides by 13 to find the price being charged is:
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P = $26/13 = $2 per battery.
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But the owner has marked up the price per battery by $1.74. So the original cost (C)
to the owner was $2 - $1.74 = $0.26 or 26 cents per battery.
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Then, at $0.26 per battery, how many batteries (B) can you get for $26.00. You can find
the number of batteries (B) by dividing the total cost of $26 by the cost per battery (C)
and you get:
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B = $26/$0.26 = 100 batteries
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Another way of looking at this problem is to let B equal the number of batteries in the case.
Since the Cost of the entire case was $26 dollars, you can find the cost to the owner
for each battery by dividing $26 by B. So the owner paid $26/B per battery.
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Then the owner increased this cost by $1.74 to establish the price he is asking for each
battery. This makes the price per battery equal to ($26/B) + $1.74
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When the owner sells 13 batteries at that price he takes in 13 times the price per battery
and the problem says that amount is $26. So we can write the equation:
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13 * [ (26/B) + 1.74] = 26
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Do the distributive multiplication on the left side and you get:
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[(13*26)/B] + [13*1.74] = 26
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Since 13*26 = 338 and 13*1.74 = 22.62 this equation simplifies to:
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[338/B] + 22.62 = 26
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Subtract the 22.62 from both sides and you get:
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[338/B] = 3.38
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Eliminate the denominator by multiplying both sides by B to get:
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338 = 3.38*B
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And finally, solve for B by dividing both sides by 3.38
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B = 338/3.38 = 100
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The answer to your problem is that there are 100 9-volt batteries in a case. Hopefully
one of these ways will clarify the problem for you. And in the way of thinking about the
economics of this situation, the owner has recovered the cost of the case of batteries
by selling 13 of them. That means the cash from the remaining 87 batteries can be used
to cover other expenses of the store plus profit. And at $2.00 per battery, that
means the owner will take in $2 * 87 or $174 above his original cost of the batteries.
(Presuming, of course, that he sells all the batteries before their expiration date.)
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