### All PSAT Math Resources

## Example Questions

### Example Question #2 : How To Find Amount Of Profit

Ricky works at a shoe shop, and earns $40 in commission for each pair of shoes he sells plus a $100 weekly salary. If Ricky receives no other money, which of the following expressions represents the total dollar amount Ricky receives for a week in which he sells *n* shoes?

**Possible Answers:**

140*n*

140 + *n*

100 + 40*n*

100 + *n*

40(100 + *n*)

**Correct answer:**

100 + 40*n*

If Ricky sells *n* shoes in a week, he earns $40*n* in commission. His salary is a constant $100 per week, so his total payout is $100 + $40*n.*

### Example Question #1 : How To Find Amount Of Profit

An entrepreneur started a company making floggles. The factory requires $1000 worth of fixed expenses to keep it running every month. She is able to produce one floggle at the cost of $4 and sell one floggle at the cost of $6. If she produces and sells 500 floggles in one month, what is her profit?

**Possible Answers:**

$1000

$2000

$0

$3000

$4000

**Correct answer:**

$0

Profit = Income - Expenditures

Income = $6/floggle times 500 floggles = $3000

Expenditures = $1000 + $4/floggle times 500 floggles = $1000 + $2000 = $3000

Profit = 3000 - 3000 = 0

### Example Question #1 : Profit Margin

You are planning a New Year’s Eve bash. For each person attending, the caterer will charge you $15 for food, $10 for beverages, $5 for service. The band charges $2000 for the entire evening. You also have to pay the venue $2500 to rent the location for the night and $3 for parking for each attendee. If you expect 500 people to attend and you would like to make a $10000 profit for planning the event, how much must each ticket cost?

**Possible Answers:**

$62

$53

$42

$33

$60

**Correct answer:**

$62

First determine total cost.

Caterer: Per person = $15 + $10 + $5 = $30 per person

Parking: Per person = $3 per person

Total per person = $33

$33 * 500 people = $16,500

Plus cost of renting venue + band = $2500 + $2000 = $4500

Total (net) cost = $16,500 + $4500 = $21,000

Total (gross) cost = net cost + profit = $21,000 + $10,000 = $31,000

Cost per ticket = Gross cost / # of attendee = $31,000 / 500 = $62

### Example Question #1 : How To Find Amount Of Profit

The Widget Company has annual revenues of $150,000. Their expenses over the same time frame was $75,000. What was the percent profit?

**Possible Answers:**

30%

25%

60%

75%

50%

**Correct answer:**

50%

Profit = Revenue – Expense

% Profit = $ Profit ÷ $ Total Revenue

% Profit = ($150,000 – $75,000) ÷ $150,000 = 50%

### Example Question #1 : How To Find Amount Of Profit

Nicki sold 20 albums at $5 each. How many albums should Minaj sell at $4.50 to earn more than Nicki?

**Possible Answers:**

23

22

24

19

25

**Correct answer:**

23

The answer is 23. 23*$4.50 = $103.50, which is more than what Nicki earned.

### Example Question #4 : How To Find Amount Of Profit

During Laura and Anna’s bake sale, 35 brownies, 12 cupcakes and 23 glasses of lemonade were sold. These goods cost $44 for the raw ingredients, and they sold for $79. What is the average profit per item?

**Possible Answers:**

$1.75

$0.25

$0.35

$0.70

$0.50

**Correct answer:**

$0.50

Total profit ($35) divided by total items (70) yields the answer of $0.50 profit per item.

### Example Question #171 : Percentage

Each wooden chair that a carpenter makes requires $20 worth of supplies. He then sells the chairs for $50 each. The carpenter recently discovered a new supplier that would allow him to spend 25% less on supplies. If he doesn't change his selling price, by what percent could the carpenter increase his profit by using the new supplier?

**Possible Answers:**

**Correct answer:**

Using $20 worth of supplies and selling the chairs for $50 each, the carpenter is originally making a profit of $30 per chair.

The new supplier would reduce costs by 25% or 1/4. One-fourth of $20 is $5, so the new supplier would be $5 less, or $15.

If the selling price is the same ($50), then the carpenter would now make a profit of $35 per chair, a change of $5.

To calculate percent increase, divide the actual change in profit by the original profit amount, and multiply the result by 100%:

(Actual Change ÷ Original Amount) * 100% = 5/30 * 100% = 500%/30 = 16.7%

### Example Question #1 : How To Find Amount Of Profit

A craftsman builds a cabinet. He pays $250 to buy the wood and miscellaneous materials for the cabinet. He spends 20 hours building the cabinet. If he values his time at $40 per hour and expects a profit margin of 50% above labor and materials, how much should he charge for the cabinet?

**Possible Answers:**

**Correct answer:**

Total Cost = Material Cost + Labor Cost + Profit

Labor Cost = $40/hour * 20 hours = $800

Profit Margin of 50% = Cost x 0.50 = $1050 x 0.50 = $525

Total Cost = $250 + $800 + $525 = $1575

### Example Question #1221 : Sat Mathematics

The cost of manufacturing a single teddy bear is $6.25. A teddy bear company sells 200 bears for $1750. What is the profit percentage per single bear?

**Possible Answers:**

60%

72%

40%

140%

28%

**Correct answer:**

40%

First we must find out what the price is for one teddy bear, manufactured by this company. Thus we divide 1750 by 200 and find that each bear costs $8.75. To find out the profit per bear, we divide 8.75 by 6.25 to arrive at 1.4. The bears are thus sold for 140% of what it costs to make them, giving a 40% profit.

### Example Question #1 : How To Find The Amount Of Sales Tax

If there is a 10% sale on an item, and then 9% sales tax is applied to that after-sale price, then what is the total cost of the item including tax as a percentage of its pre-sale sticker price?

**Possible Answers:**

101%

81.9%

99.2%

98.1%

99%

**Correct answer:**

98.1%

A 10% sale means that the post-sale price of the item is now 90%, or 0.9 of the original cost of the item. We then apply 9% sales tax by multiplying the 0.9 by 109%, or 1.09. 0.9 * 1.09 = .981, so the total cost of the item is **98.1%** of the original pre-sale sticker price.

For percentage problems that do not deal with a specific starting number, it is always helpful to plug in 100 for the starting number. Here, we would then have a post-sale price of 90 dollars, and if we calculate the sales tax for the 90-dollar item it would be 90 * 0.09 = $8.10. THis gives us a total cost of 90 + 8.10 = $98.10, or 98.1% of the original 100-dollar price.

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