Percentage - PSAT Math
Card 1 of 700
If the length of a rectangle is increased by thirty percent, which of the following most closely approximates the percent by which the rectangle's width must decrease, so that the area of the rectangle remains unchanged?
If the length of a rectangle is increased by thirty percent, which of the following most closely approximates the percent by which the rectangle's width must decrease, so that the area of the rectangle remains unchanged?
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If the price of a TV was decreased from $3,000 to $1,800, by what percent was the price decreased?
If the price of a TV was decreased from $3,000 to $1,800, by what percent was the price decreased?
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The price was lowered by $1,200 which is 40% of $3,000.
The price was lowered by $1,200 which is 40% of $3,000.
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If a rectangle's length decreases by fifteen percent, and its width decreases by twenty percent, then by what percent does the rectangle's area decrease?
If a rectangle's length decreases by fifteen percent, and its width decreases by twenty percent, then by what percent does the rectangle's area decrease?
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Let's call the original length and width of the rectangle 
and 
, respectively.
The initial area, 
, of the rectangle is equal to the product of the length and the width. We can represent this with the following equation:
Next, let 
and 
represent the length and width, respectively, after they have been decreased. The final area will be equal to 
, which will be equal to the product of the final length and width.
We are asked to find the change in the area, which essentially means we want to compare 
and 
. In order to do this, we will need to find an expression for 
in terms of 
and 
. We can rewrite 
and 
in terms of 
and 
.
First, we are told that the length is decreased by fifteen percent. We can think of the full length as 100% of the length. If we take away fifteen percent, we are left with 100 – 15, or 85% of the length. In other words, the final length is 85% of the original length. We can represent 85% as a decimal by moving the decimal two places to the left.
= 85% of 
= 
Similarly, if we decrease the width by 20%, we are only left with 80% of the width.
= 80% of 
= 
We can now express the final area in terms of 
and 
by substituting the expressions we just found for the final length and width.
= (
)(
) = 
Lastly, let's apply the formula for percent of change, which will equal the change in the area divided by the original area. The change in the area is equal to the final area minus the original area.
percent change = 
(100%)
=
(100%)
=
(100%) = –0.32(100%) = –32%
The negative sign indicates that the rectangle's area decreased. The change in the area was a decrease of 32%.
The answer is 32.
Let's call the original length and width of the rectangle
The initial area,
Next, let
We are asked to find the change in the area, which essentially means we want to compare
First, we are told that the length is decreased by fifteen percent. We can think of the full length as 100% of the length. If we take away fifteen percent, we are left with 100 – 15, or 85% of the length. In other words, the final length is 85% of the original length. We can represent 85% as a decimal by moving the decimal two places to the left.
Similarly, if we decrease the width by 20%, we are only left with 80% of the width.
We can now express the final area in terms of
Lastly, let's apply the formula for percent of change, which will equal the change in the area divided by the original area. The change in the area is equal to the final area minus the original area.
percent change =
=
=
The negative sign indicates that the rectangle's area decreased. The change in the area was a decrease of 32%.
The answer is 32.
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55 and 1/2% of 23 is about what?
55 and 1/2% of 23 is about what?
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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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Write as a fraction: 22%
Write as a fraction: 22%
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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?
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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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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?
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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?
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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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Find the simplified fraction for 
Find the simplified fraction for
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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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You have 2 fair dice that each have 6 faces. On one roll, what's the probability that both dice land on an even number?
You have 2 fair dice that each have 6 faces. On one roll, what's the probability that both dice land on an even number?
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In order to find the probability of rolling two even numbers on 2 dice we need to find the probability of each dice having an even number on the roll and then multiply them together.
The probability of rolling an even number is
because 2, 4, and 6 are even numbers which goes in the numerator and there are 6 total numbers which goes in the denominator. After this we reduce the fraction and get one half. Then we need to muliply this by probability of the second dice having an even number.
In order to find the probability of rolling two even numbers on 2 dice we need to find the probability of each dice having an even number on the roll and then multiply them together.
The probability of rolling an even number is
because 2, 4, and 6 are even numbers which goes in the numerator and there are 6 total numbers which goes in the denominator. After this we reduce the fraction and get one half. Then we need to muliply this by probability of the second dice having an even number.
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What is 15% of a $16.73 bill?
What is 15% of a $16.73 bill?
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We can re write 15% as a fraction and then use proportions to solve.
From here we cross multiply and divide to solve for 
.
We can re write 15% as a fraction and then use proportions to solve.
From here we cross multiply and divide to solve for
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If a test has a total of 
questions and 
of the questions are multiple choice, how many questions are multiple choice?
If a test has a total of
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To solve this problem we set up a ratio. We want to find 
of 
. Therefore, we set up the following ratio:
In the case 
represents the number of questions that are multiple choice. From here we cross multiply and divide.
To solve this problem we set up a ratio. We want to find
In the case
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If there are 3 boys in a class and 7 girls. What percent of the class is made up of boys?
If there are 3 boys in a class and 7 girls. What percent of the class is made up of boys?
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To solve this problem we set up a ratio of part of total. The part is the number of boys in the class and the total is the number of boys and girls in the class.
now to find the percent we can multiply this fraction by 10/10
From here we can see that it is 30%
To solve this problem we set up a ratio of part of total. The part is the number of boys in the class and the total is the number of boys and girls in the class.
now to find the percent we can multiply this fraction by 10/10
From here we can see that it is 30%
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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?
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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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Marker Colors Students Blue 13 Pink 10 Orange 5 Brown 5 Green 7
The above chart shows the number of students in a class who chose each of the five marker colors available.
What percentage of the class chose a green marker?
| Marker Colors | Students |
|---|---|
| Blue | 13 |
| Pink | 10 |
| Orange | 5 |
| Brown | 5 |
| Green | 7 |
The above chart shows the number of students in a class who chose each of the five marker colors available.
What percentage of the class chose a green marker?
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To figure out what percentage of the class chose green markers, you must first figure out what fraction of the class chose green markers. Then, you must convert that fraction into a percentage.
Figure out the fraction:
7 students chose green markers
40 students total
Fraction of students who chose green: 
To convert this fraction to a percentage, you must multiply the fraction times 100, then divide the numerator by the denominator. You multiply the fraction times 100 because in order to figure out the percent, you must figure out what the fraction means "for (per) every hundred (cent)".
Multiply times 100
Therefore, the answer is 
.
To figure out what percentage of the class chose green markers, you must first figure out what fraction of the class chose green markers. Then, you must convert that fraction into a percentage.
Figure out the fraction:
7 students chose green markers
40 students total
Fraction of students who chose green:
To convert this fraction to a percentage, you must multiply the fraction times 100, then divide the numerator by the denominator. You multiply the fraction times 100 because in order to figure out the percent, you must figure out what the fraction means "for (per) every hundred (cent)".
Multiply times 100
Therefore, the answer is
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The pie chart illustrates how Carla allocates her money each week.
If she spends $200 on groceries each week, how much does she spend on rent?
The pie chart illustrates how Carla allocates her money each week.
If she spends $200 on groceries each week, how much does she spend on rent?
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1. 20% of Carla's whole budget is equal to $200. With this information, one can find Carla's weekly budget.
Set up the equation: 0.2b = 200 (b = budget).
b = 200/0.2 = 1000 = Carla's weekly budget
2. To find the amount Carla spends for rent, one needs to find what 35% of $1000 is.
0.35 x 1000 = 350
3. Because Carla spends 35% of her total budget on rent, she spends $350 on rent.
1. 20% of Carla's whole budget is equal to $200. With this information, one can find Carla's weekly budget.
Set up the equation: 0.2b = 200 (b = budget).
b = 200/0.2 = 1000 = Carla's weekly budget
2. To find the amount Carla spends for rent, one needs to find what 35% of $1000 is.
0.35 x 1000 = 350
3. Because Carla spends 35% of her total budget on rent, she spends $350 on rent.
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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?
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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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Maria was shopping for a camera and found one that was on sale for 30% off. As she went to pay for it, the store announced an instant sale that took an additional 10% off all items. If the final price Maria paid was $207.27, what was the original price (before all discounts) of the camera?
Maria was shopping for a camera and found one that was on sale for 30% off. As she went to pay for it, the store announced an instant sale that took an additional 10% off all items. If the final price Maria paid was $207.27, what was the original price (before all discounts) of the camera?
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To reconstruct an original price from a sale price, use:
Original Price – Original Price * Mark-down-percent = Sale Price, or
Original Price * (1 - Mark-down-percent) = Sale Price
To do a double mark-down problem, we must do this twice. For the 10%:
Original Sale Price * (1 – 10%) = $207.27
Original Sale Price = $207.27/0.9 = $230.30.
For the pre-all-discount price,
Original Price * (1 – 30%) = $230.30
Original Price = $230.30/0.7 = $329.00.
To reconstruct an original price from a sale price, use:
Original Price – Original Price * Mark-down-percent = Sale Price, or
Original Price * (1 - Mark-down-percent) = Sale Price
To do a double mark-down problem, we must do this twice. For the 10%:
Original Sale Price * (1 – 10%) = $207.27
Original Sale Price = $207.27/0.9 = $230.30.
For the pre-all-discount price,
Original Price * (1 – 30%) = $230.30
Original Price = $230.30/0.7 = $329.00.
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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?
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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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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?
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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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