Percentage - PSAT Math
Card 0 of 20
Find the simplified fraction for 
Find the simplified fraction for
For any percent 
we can write it as a fraction in the form 
So we can write 
as 
Then we simplify
So our simplified answer is 
For any percent
So we can write
Then we simplify
So our simplified answer is
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Write 7.5% as a fraction.
Write 7.5% as a fraction.
First convert the percentage to a decimal:
7.5% = .075
Then turn this into a fraction:
.075 = 75/1000
Simplify by dividing the numerator and denominator by 25:
75/1000 = 3/40
First convert the percentage to a decimal:
7.5% = .075
Then turn this into a fraction:
.075 = 75/1000
Simplify by dividing the numerator and denominator by 25:
75/1000 = 3/40
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Write as a fraction: 22%
Write as a fraction: 22%
22% = 22/100
Divide everything by 2:
22/100 = 11/50
11 is a prime number, so this is as reduced as this fraction can get.
22% = 22/100
Divide everything by 2:
22/100 = 11/50
11 is a prime number, so this is as reduced as this fraction can get.
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25% of 64 is equal to 5% of what number?
25% of 64 is equal to 5% of what number?
25% of 64 is 16 (you can find this with a calculator by 0.25 * 64). Divide 16 by 0.05 (or 1/20) to get the value of the number 16 is 5% of. (Or mental math of 16 * 20)
25% of 64 is 16 (you can find this with a calculator by 0.25 * 64). Divide 16 by 0.05 (or 1/20) to get the value of the number 16 is 5% of. (Or mental math of 16 * 20)
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When y is decreased by ten percent, the result is equal to fifteen percent of x. Assuming both x and y are nonzero, what is the ratio of x to y?
When y is decreased by ten percent, the result is equal to fifteen percent of x. Assuming both x and y are nonzero, what is the ratio of x to y?
The problem states that decreasing y by ten percent gives us the same thing as taking fifteen percent of x. We need to find an expression for decreasing y by ten percent, and an expression for fifteen percent of x, and then set these two things equal.
If we were to decrease y by ten percent, we would be left with ninety percent of y (because the percentages must add to one hundred percent). We could write ninety percent of y as 0.90_y_ = (90/100)y = (9/10)y. Remember, when converting from a percent to a decimal, we need to move the decimal two places to the left.
Similarly, we can write 15% of x as 0.15_x_ = (15/100)x = (3/20)x.
Now, we set these two expressions equal to one another.
(9/10)y = (3/20)x
Multiply both sides by 20 to eliminate fractions.
18_y_ = 3_x_
The question asks us to find the ratio of x to y, which is equal to x/y. Thus, we must rearrange the equation above until we have x/y by itself on one side.
18_y_ = 3_x_
Divide both sides by 3.
6_y_ = x
Divide both sides by y.
6 = x/y
Thus, the ratio of x to y is 6.
The answer is 6.
The problem states that decreasing y by ten percent gives us the same thing as taking fifteen percent of x. We need to find an expression for decreasing y by ten percent, and an expression for fifteen percent of x, and then set these two things equal.
If we were to decrease y by ten percent, we would be left with ninety percent of y (because the percentages must add to one hundred percent). We could write ninety percent of y as 0.90_y_ = (90/100)y = (9/10)y. Remember, when converting from a percent to a decimal, we need to move the decimal two places to the left.
Similarly, we can write 15% of x as 0.15_x_ = (15/100)x = (3/20)x.
Now, we set these two expressions equal to one another.
(9/10)y = (3/20)x
Multiply both sides by 20 to eliminate fractions.
18_y_ = 3_x_
The question asks us to find the ratio of x to y, which is equal to x/y. Thus, we must rearrange the equation above until we have x/y by itself on one side.
18_y_ = 3_x_
Divide both sides by 3.
6_y_ = x
Divide both sides by y.
6 = x/y
Thus, the ratio of x to y is 6.
The answer is 6.
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Convert 62% into simplified fraction form.
Convert 62% into simplified fraction form.
To convert a percent into a fraction, simply divide by 100 and reduce. In our case, 62 and 100 have the common factor of 2, so solving and simplification are as follows:
To convert a percent into a fraction, simply divide by 100 and reduce. In our case, 62 and 100 have the common factor of 2, so solving and simplification are as follows:
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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?
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?
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%
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%
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A sunglasses kiosk at the mall makes a $50 profit for every 6 pairs of sunglasses it sells. How many pairs of sunglasses must it sell to earn $1000 profit?
A sunglasses kiosk at the mall makes a $50 profit for every 6 pairs of sunglasses it sells. How many pairs of sunglasses must it sell to earn $1000 profit?
Divide the profit per 6 pairs into the total desired profit $1000/$50 = 20.
Multiply 20 by 6 sunglasses = 120 sunglasses. Or use 6/50 = x/1000 and solve for x.
Divide the profit per 6 pairs into the total desired profit $1000/$50 = 20.
Multiply 20 by 6 sunglasses = 120 sunglasses. Or use 6/50 = x/1000 and solve for x.
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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?
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?
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._
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._
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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?
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?
Profit = Income - Expenditures
Income = $6/floggle times 500 floggles = $3000
Expenditures = $1000 + $4/floggle times 500 floggles = $1000 + $2000 = $3000
Profit = 3000 - 3000 = 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
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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?
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?
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
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
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The Widget Company has annual revenues of $150,000. Their expenses over the same time frame was $75,000. What was the percent 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?
Profit = Revenue – Expense
% Profit = $ Profit ÷ $ Total Revenue
% Profit = ($150,000 – $75,000) ÷ $150,000 = 50%
Profit = Revenue – Expense
% Profit = $ Profit ÷ $ Total Revenue
% Profit = ($150,000 – $75,000) ÷ $150,000 = 50%
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Nicki sold 20 albums at $5 each. How many albums should Minaj sell at $4.50 to earn more than Nicki?
Nicki sold 20 albums at $5 each. How many albums should Minaj sell at $4.50 to earn more than Nicki?
The answer is 23. 23*$4.50 = $103.50, which is more than what Nicki earned.
The answer is 23. 23*$4.50 = $103.50, which is more than what Nicki earned.
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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?
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?
Total profit ($35) divided by total items (70) yields the answer of $0.50 profit per item.
Total profit ($35) divided by total items (70) yields the answer of $0.50 profit per item.
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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?
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?
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
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
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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?
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?
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.
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.
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55 and 1/2% of 23 is about what?
55 and 1/2% of 23 is about what?
55 and 1/2% can be written as a decimal: 0.555. To see what number is about 55.5% of 23, multiply 0.555 by 23. Answer: 12.765 or about 13.
Another route is to say that 55.5% is about half of 23. Half of 23 is 11.5. Since 55.5% is greater than 50%, 13 is the logical choice instead of 11.
55 and 1/2% can be written as a decimal: 0.555. To see what number is about 55.5% of 23, multiply 0.555 by 23. Answer: 12.765 or about 13.
Another route is to say that 55.5% is about half of 23. Half of 23 is 11.5. Since 55.5% is greater than 50%, 13 is the logical choice instead of 11.
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Let x and y be numbers such that x and y are both nonzero, and x > y. If half of x is equal to thirty percent of the positive difference between x and y, then what is the ratio of x to y?
Let x and y be numbers such that x and y are both nonzero, and x > y. If half of x is equal to thirty percent of the positive difference between x and y, then what is the ratio of x to y?
We need to find expressions for fifty percent of x and for thirty percent of the positive difference between x and y. Then, we can set these two expressions equal to each other and determine the ratio of x to y.
Fifty percent of x is equal to one-half of x, which is the same as multiplying x by 0.50.
50% of x = 0.5_x_
Thirty percent of the positive difference between x and y means that we need to multiply the positive difference between x and y by thirty percent. Because x > y, the positive difference between x and y is equal to x – y. We then need to take thirty percent of the quantity x – y. Remember that to convert from a percent to a decimal, we move the decimal two spaces to the left. Therefore, 30% = 0.30. We can now multiply this by (x – y).
30% of x – y = 0.30(x – y)
Now, we set the two expressions equal to one another.
0.5_x_ = 0.30(x – y)
Distribute the right side.
0.5_x_ = 0.3_x_ – 0.3_y_
The ratio of x to y is represent by x/y. Thus, we want to group the x and y terms on opposite sides of the equations, and then divide both sides by y.
0.5_x_ = 0.3_x_ – 0.3_y_
Subtract 0.3_x_ from both sides.
0.2_x_ = –0.3_y_
Divide both sides by 0.2
x = (–0.3/0.2)y
Divide both sides by y to find x/y.
x/y = (–0.3/0.2) = –1.5.
Because the answers are in fractions, we want to rewrite –1.5 as a fraction. We can write –1.5 as –1.5/1 and then mutiply the top and bottom by 2.
(–1.5/1)(2/2) = –3/2
The answer is –3/2
We need to find expressions for fifty percent of x and for thirty percent of the positive difference between x and y. Then, we can set these two expressions equal to each other and determine the ratio of x to y.
Fifty percent of x is equal to one-half of x, which is the same as multiplying x by 0.50.
50% of x = 0.5_x_
Thirty percent of the positive difference between x and y means that we need to multiply the positive difference between x and y by thirty percent. Because x > y, the positive difference between x and y is equal to x – y. We then need to take thirty percent of the quantity x – y. Remember that to convert from a percent to a decimal, we move the decimal two spaces to the left. Therefore, 30% = 0.30. We can now multiply this by (x – y).
30% of x – y = 0.30(x – y)
Now, we set the two expressions equal to one another.
0.5_x_ = 0.30(x – y)
Distribute the right side.
0.5_x_ = 0.3_x_ – 0.3_y_
The ratio of x to y is represent by x/y. Thus, we want to group the x and y terms on opposite sides of the equations, and then divide both sides by y.
0.5_x_ = 0.3_x_ – 0.3_y_
Subtract 0.3_x_ from both sides.
0.2_x_ = –0.3_y_
Divide both sides by 0.2
x = (–0.3/0.2)y
Divide both sides by y to find x/y.
x/y = (–0.3/0.2) = –1.5.
Because the answers are in fractions, we want to rewrite –1.5 as a fraction. We can write –1.5 as –1.5/1 and then mutiply the top and bottom by 2.
(–1.5/1)(2/2) = –3/2
The answer is –3/2
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If 
of 
is equal to 
of 
, and 
of 
is equal to 
of 
, then what percent of 
is 
?
If
We are told that 50% of x is equal to 25% of y. We need to represent these two pieces of information as algebraic expressions. We can convert 50% and 25% to decimals by moving the decimals two places to the left. Thus, 50% = 0.50, and 25% = 0.25. To find 50% of x, we multiply x by 0.50. In other words, 50% of x = 0.50_x_. Likewise, 25% of y = 0.25_y_. We now set 0.50_x_ and 0.25_y_ equal to one another.
0.50_x_ = 0.25_y_
Let's divide both sides by 0.25 to get rid of decimals.
2_x_ = y
Next, we are told that 40% of y is equal to 60% of z. We will represent 40% and 60% as 0.40 and 0.60, respectively. Thus, we can write the following equation:
0.40_y_ = 0.60_z_
Ultimately, we are asked to find x as a percentage of z. This means we want to find an equation with x and z, but not y. If we solve for y in the second equation, and then substitute this value into the first, we can eliminate y.
Let's take the equation 0.40_y_ = 0.60_z_ and divide both sides by 0.40.
y = 1.5_z_
Now, we can take 1.5_z_ and substitute this for y in the first equation.
2_x_ = 1.5_z_
In order to find x as a percent of z, we must solve for x in terms of z. This means we must divide both sides of the equation by 2.
x = 0.75_z_
x is 0.75 times z. We can represent 0.75 as 75%, because in order to convert from a decimal to a percent, we need to move the decimal two spaces to the right. Therefore, if x = 0.75_z_, then x = 75% of z.
The answer is 75.
We are told that 50% of x is equal to 25% of y. We need to represent these two pieces of information as algebraic expressions. We can convert 50% and 25% to decimals by moving the decimals two places to the left. Thus, 50% = 0.50, and 25% = 0.25. To find 50% of x, we multiply x by 0.50. In other words, 50% of x = 0.50_x_. Likewise, 25% of y = 0.25_y_. We now set 0.50_x_ and 0.25_y_ equal to one another.
0.50_x_ = 0.25_y_
Let's divide both sides by 0.25 to get rid of decimals.
2_x_ = y
Next, we are told that 40% of y is equal to 60% of z. We will represent 40% and 60% as 0.40 and 0.60, respectively. Thus, we can write the following equation:
0.40_y_ = 0.60_z_
Ultimately, we are asked to find x as a percentage of z. This means we want to find an equation with x and z, but not y. If we solve for y in the second equation, and then substitute this value into the first, we can eliminate y.
Let's take the equation 0.40_y_ = 0.60_z_ and divide both sides by 0.40.
y = 1.5_z_
Now, we can take 1.5_z_ and substitute this for y in the first equation.
2_x_ = 1.5_z_
In order to find x as a percent of z, we must solve for x in terms of z. This means we must divide both sides of the equation by 2.
x = 0.75_z_
x is 0.75 times z. We can represent 0.75 as 75%, because in order to convert from a decimal to a percent, we need to move the decimal two spaces to the right. Therefore, if x = 0.75_z_, then x = 75% of z.
The answer is 75.
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To get on the ballot for the student body president at Harding High School, a student must turn in a petition with the signatures of 8% of the students from each of the four classes - freshman, sophomore, junior, and senior. There are 342 freshmen, 312 sophomores, 270 juniors, and 268 seniors enrolled at McKinley.
Tom has a petition with the signatures of 25 students from each of the four classes. Can he get on the ballot with the signatures he has, and if not, why not?
To get on the ballot for the student body president at Harding High School, a student must turn in a petition with the signatures of 8% of the students from each of the four classes - freshman, sophomore, junior, and senior. There are 342 freshmen, 312 sophomores, 270 juniors, and 268 seniors enrolled at McKinley.
Tom has a petition with the signatures of 25 students from each of the four classes. Can he get on the ballot with the signatures he has, and if not, why not?
In order to answer the question, we must find out the percent of each class that has signed Tom's petition, and compare it to 8%.
Freshmen: 
have signed.
Sophomores: 
have signed.
Juniors: 
have signed.
Seniors: 
have signed.
Tom has the necessary signatures from members of the top three classes, but he cannot get on the ballot yet because he has not gathered enough signatures from freshmen.
In order to answer the question, we must find out the percent of each class that has signed Tom's petition, and compare it to 8%.
Freshmen:
Sophomores:
Juniors:
Seniors:
Tom has the necessary signatures from members of the top three classes, but he cannot get on the ballot yet because he has not gathered enough signatures from freshmen.
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