Algebra 1 : How to find amount of profit

Study concepts, example questions & explanations for Algebra 1

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Example Questions

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Example Question #1 : How To Find Amount Of Profit

A shirt is purchased by a store for $10.  The whole cost to market and sell the shirt is $3.  If it is sold for $20, what is the profit percentage made by the store (to the closest whole number)?

Possible Answers:

Correct answer:

Explanation:

 First, note that the complete cost of the shirt is .  Therefore, the store makes  in profit on the sale of the shirt.  At this point, the problem merely becomes one of percentage change.  They make  percent profit— approximately  or .

Example Question #2 : How To Find Amount Of Profit

The total cost to sell a given tie is $30.  If its original sale price was $45 but was marked down by 10%, how much profit was made on the sale after the markdown?

Possible Answers:

Correct answer:

Explanation:

The first thing to do is figure out the sale price.  There are two ways to do this:

First way: .

Second way: 

(The second way is like saying, "The new price is 90% of the original."  This is really the easiest way to do problems like this and should be learned.)

Now, to find the profit, merely subtract the original amount, namely : .

Example Question #3 : How To Find Amount Of Profit

Jessica sells cookies for $2 a piece.  She has calculated that she makes a 23% profit on each cookie.  How much does each cookie cost her to produce?

Possible Answers:

Correct answer:

Explanation:

Be careful. Based on the question, we apply the percent profit to the her cost to produce a cookie NOT to the $2.00 in revenue.  So our equation would be:

where represents how much it costs Jessica to make a cookie.

We can simplify this to:

So it would cost Jessica $1.63 to make a cookie.

Example Question #1 : How To Find Amount Of Profit

An item selling for $15.40 makes a 10% profit.  How many of these items must be sold in order to make a total profit of $10,000?

Possible Answers:

Correct answer:

Explanation:

Be careful with this calculation.  If an item is making 10% profit, that means that it is making that profit on the original price.  

Therefore, if  is the original price, we can write:

.  

Solving for , we get .  

This means that the profit per item is $1.40.  Now, divide 10,000 by 1.4 and get 7,142.857.  Since you cannot sell partial items, you will need to sell 7,143 items in order to get a $10,000 profit.

Example Question #5 : How To Find Amount Of Profit

An item being sold for $17.10 makes a 14% profit. What is its original price?

Possible Answers:

Correct answer:

Explanation:

If an item is selling for $17.10, its original price  can be found by the following equation:  

Solving for , we get $15.00 as the original price.

Example Question #5 : How To Find Amount Of Profit

An item is being sold at $22 even though that represents a 20% loss on the original price.  What is the original price?

Possible Answers:

Correct answer:

Explanation:

If the item is sold at a 20% loss, this means that the retailer is getting only 80% of the original price .  This can be represented as

.  

Solving for , we get


Example Question #2 : How To Find Amount Of Profit

An item that costs $30 to purchase and retail is sold for 15% profit.  How many need to be sold to make $25,000 profit?

Possible Answers:

Correct answer:

Explanation:

There are two steps to this problem.  First, we must calculate how much profit is made per item.  The general form of the question we are asking is, "How much is 15% of $30?"  This can be rewritten:

Now, if you make $4.5 per item, you need to divide the total profit desired ($25,000) by $4.5:

Be careful!  You need to sell 5,556 items, NOT 5,555.  At 5,555, you will have only made $24,997.5 in profit. 

Example Question #5 : How To Find Amount Of Profit

A store sells an item for $37, making a 17% profit.  What is this profit in dollars and cents?

Possible Answers:

$31.62

$9.32

$30.43

$6.29

$5.38

Correct answer:

$5.38

Explanation:

This problem implies that some original price  was marked up by .  

This can be represented in an equation as , where  is the final sale price. 

Therefore, we can rewrite the equation:

Divide both sides by 1.17:

Rounding, we can say that the cost of the item is $31.62.  Subtract this from $37 to get a profit of $5.38.

Example Question #4 : How To Find Amount Of Profit

Possible Answers:

Correct answer:

Explanation:

Example Question #3 : How To Find Amount Of Profit

Jimmy's Pizza and Pasta agreed to do a fundraising event at their restaurant with the local high school.  of all proceeds will be donated to help buy new textbooks. The fundraising event generated an income of . How much money was raised for new textbooks?

Possible Answers:

Correct answer:

Explanation:

 of the total proceeds can be calculated as such:

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