Whole and Part - PSAT Math
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A school is made up of 400 students. Each student must belong to one of the four clubs shown in the chart below. How many students are in chorus?
A school is made up of 400 students. Each student must belong to one of the four clubs shown in the chart below. How many students are in chorus?
You must first determine the percentage of the students in chorus. To do this, subtract the other percentages from 100: 100 – (35 + 29 + 24) = 12.
Therefore, 12% of the 400 students at this school attend chorus.
To determine the number of students in the chorus, multiply .12 (12%) by 400.
0.12(400) = 48
You must first determine the percentage of the students in chorus. To do this, subtract the other percentages from 100: 100 – (35 + 29 + 24) = 12.
Therefore, 12% of the 400 students at this school attend chorus.
To determine the number of students in the chorus, multiply .12 (12%) by 400.
0.12(400) = 48
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Your friend has 100 pounds of bacon and offers to share 45% of it with you. If you promised your mom 30% and your cousin 25% of your share, how many pounds of bacon do you end up with?
Your friend has 100 pounds of bacon and offers to share 45% of it with you. If you promised your mom 30% and your cousin 25% of your share, how many pounds of bacon do you end up with?
Your share = 45% of 100 pounds of bacon = .45 * 100 = 45 pounds
For mom and cousin = 30% + 25% = 55%
Percent left for you = 100% - 55% = 45%
45% of 45 pounds = .45 * 45 = 20.25 pounds
Your share = 45% of 100 pounds of bacon = .45 * 100 = 45 pounds
For mom and cousin = 30% + 25% = 55%
Percent left for you = 100% - 55% = 45%
45% of 45 pounds = .45 * 45 = 20.25 pounds
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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?
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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Three salesmen, Gor, Levon, and Raffi, competed to sell the highest number of cars in the month of August. A total of 250 cars were sold.
Gor sold 100 cars. Levon sold 62% of the remaining cars, and Raffi sold the rest.
How many cars did Raffi sell?
Three salesmen, Gor, Levon, and Raffi, competed to sell the highest number of cars in the month of August. A total of 250 cars were sold.
Gor sold 100 cars. Levon sold 62% of the remaining cars, and Raffi sold the rest.
How many cars did Raffi sell?
We first subtract the 100 cars that Gor sold from the total of 250 sold. We are left with 150 cars, and we know that Levon sold 62% of them. 100% – 62% = 38%. Hence, Raffi sold 38% of 150 cars. 150 * 0.38 = 57
We first subtract the 100 cars that Gor sold from the total of 250 sold. We are left with 150 cars, and we know that Levon sold 62% of them. 100% – 62% = 38%. Hence, Raffi sold 38% of 150 cars. 150 * 0.38 = 57
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A container has ten liters of a twenty percent sucrose solution by volume. How many liters of the solution should be removed from the container and then replaced by the same volume of a forty percent sucrose solution, so that the final solution is ten liters of a twenty-five percent sucrose solution?
A container has ten liters of a twenty percent sucrose solution by volume. How many liters of the solution should be removed from the container and then replaced by the same volume of a forty percent sucrose solution, so that the final solution is ten liters of a twenty-five percent sucrose solution?
The final solution is going to have a concentration of twenty-five percent and a volume of 10 liters. The amount of sucrose in the solution is equal to the concentration (expressed as a decimal) multiplied by the total volume. Therefore, the final solution will have 25% • 10 = 0.25 • 10 = 2.5 liters of sucrose.
Let x be the amount of the solution that is removed and then replaced by the forty percent solution. The amount of twenty percent solution that will remain will be equal to 10 – x, because the final solution will still have ten liters. (The amount removed is replaced with the same amount, so the final volume of the solution is the same.)
So we have to get 2.5 liters of sucrose from the twenty percent solution and the forty percent solution combined. The amount of sucrose we will get from the twenty percent solution equals the volume of the twenty percent solution (which we established will be 10 – x) multiplied by twenty percent as a decimal.
Amount of sucrose from 20% solution = 0.20 • (10 – x)
The amount of sucrose we get from the forty percent solution will equal the product of x and forty percent (since we defined x as the amount of forty percent solution).
Amount of sucrose from 40% solution = 0.40x
Now, we need to add the amount of sucrose from the 20% and the 40% solutions, and then set this equal to 2.5, because ultimately we will have 2.5 liters of sucrose in the solution. We can write the equation as follows and then solve for x:
0.20 • (10 – x) + 0.40x = 2.5
Here is a table that we can also use to summarize the information discussed above.
0.20 • (10 – x) + 0.40x = 2.5
Distribute.
2 – 0.2x + 0.4x = 2.5
Combine x terms.
2 + 0.2x = 2.5
Subtract 2 from both sides.
0.2x = 0.5
Divide both sides by 0.2.
x = 2.5 liters
The answer is 2.5 liters.
The final solution is going to have a concentration of twenty-five percent and a volume of 10 liters. The amount of sucrose in the solution is equal to the concentration (expressed as a decimal) multiplied by the total volume. Therefore, the final solution will have 25% • 10 = 0.25 • 10 = 2.5 liters of sucrose.
Let x be the amount of the solution that is removed and then replaced by the forty percent solution. The amount of twenty percent solution that will remain will be equal to 10 – x, because the final solution will still have ten liters. (The amount removed is replaced with the same amount, so the final volume of the solution is the same.)
So we have to get 2.5 liters of sucrose from the twenty percent solution and the forty percent solution combined. The amount of sucrose we will get from the twenty percent solution equals the volume of the twenty percent solution (which we established will be 10 – x) multiplied by twenty percent as a decimal.
Amount of sucrose from 20% solution = 0.20 • (10 – x)
The amount of sucrose we get from the forty percent solution will equal the product of x and forty percent (since we defined x as the amount of forty percent solution).
Amount of sucrose from 40% solution = 0.40x
Now, we need to add the amount of sucrose from the 20% and the 40% solutions, and then set this equal to 2.5, because ultimately we will have 2.5 liters of sucrose in the solution. We can write the equation as follows and then solve for x:
0.20 • (10 – x) + 0.40x = 2.5
Here is a table that we can also use to summarize the information discussed above.
0.20 • (10 – x) + 0.40x = 2.5
Distribute.
2 – 0.2x + 0.4x = 2.5
Combine x terms.
2 + 0.2x = 2.5
Subtract 2 from both sides.
0.2x = 0.5
Divide both sides by 0.2.
x = 2.5 liters
The answer is 2.5 liters.
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A total of 200,000 votes were cast for two opposing candidates. If the losing candidate received 40% of the vote, how many votes did the winning candidate receive?
A total of 200,000 votes were cast for two opposing candidates. If the losing candidate received 40% of the vote, how many votes did the winning candidate receive?
60% of 200,000 is 120,000
0.6 * 200,000 = 120,000
60% of 200,000 is 120,000
0.6 * 200,000 = 120,000
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Becky and Jason are running for class president, and each of the 30 students in the class voted. Becky received 60% of the votes. How many students voted for Jason?
Becky and Jason are running for class president, and each of the 30 students in the class voted. Becky received 60% of the votes. How many students voted for Jason?
If Becky received 60% of the vote, Jason must have received 40% of the vote. 40% is equal to 0.40. By multiplying the number of votes times the percentage, we can calculate how many votes Jason received.
0.40 * 30 = 12.
If Becky received 60% of the vote, Jason must have received 40% of the vote. 40% is equal to 0.40. By multiplying the number of votes times the percentage, we can calculate how many votes Jason received.
0.40 * 30 = 12.
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There are 
pounds of cargo currently on a ship. After 
pounds have been taken from the ship and transferred to a warehouse, then, in terms of 
and 
, what percent of cargo is still on the ship?
There are
If p is the number of pounds of cargo that is initially on the ship and m is the number of pounds of cargo that we transfer (or remove from the ship), we can find how many pounds of cargo are still on the ship after the transfer by the expression p – m. In order to model this as a percent, we would have to form a fraction, using the initial pounds of cargo, p, as the whole amount and p – m as the fractional part.
So,
we would get 
as our fraction.
However, this problem asks us to find the percent, so we would simply multiply by 100
![\dpi{100} \small \left [\frac{100\left (p-m \right )}{p} \right ]%](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/18571/gif.latex)
will get our answer into percent form.
If p is the number of pounds of cargo that is initially on the ship and m is the number of pounds of cargo that we transfer (or remove from the ship), we can find how many pounds of cargo are still on the ship after the transfer by the expression p – m. In order to model this as a percent, we would have to form a fraction, using the initial pounds of cargo, p, as the whole amount and p – m as the fractional part.
So,
we would get
However, this problem asks us to find the percent, so we would simply multiply by 100
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I ate 30% of an entire pizza. My friend Sally ate 20% of the remaining pizza. What percentage of the original pizza is left?
I ate 30% of an entire pizza. My friend Sally ate 20% of the remaining pizza. What percentage of the original pizza is left?
After I eat 30% of the pizza, 70%, or 0.7, is left. Sally eats 20%, or 0.2 of that. So to compute how much of the original pizza Sally has eaten, we must multiply 0.7 by 0.2. We will arrive with 0.14 or 14%. Thus we subtract my the 30% of the pizza I ate and the 14% of the pizza Sally ate from 100% or the original whole, and we will arrive with 56%.
After I eat 30% of the pizza, 70%, or 0.7, is left. Sally eats 20%, or 0.2 of that. So to compute how much of the original pizza Sally has eaten, we must multiply 0.7 by 0.2. We will arrive with 0.14 or 14%. Thus we subtract my the 30% of the pizza I ate and the 14% of the pizza Sally ate from 100% or the original whole, and we will arrive with 56%.
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The above graph represents the results of a general election for mayor of Washington City. Hall is a Republican; Johns is a Democrat; the other three are independents.
5,328 people voted for independent candidates. Which is the best estimate for the number of people who voted for Hall?
The above graph represents the results of a general election for mayor of Washington City. Hall is a Republican; Johns is a Democrat; the other three are independents.
5,328 people voted for independent candidates. Which is the best estimate for the number of people who voted for Hall?
The green wedge, which represents Hall, is about 45% of the circle. The three wedges representing independents Carson, Franklin, and Lamont - dark red, bright red, and turquoise, respectively - together comprise about 40% of the circle. We can set up, and solve for the unknown in, a proportion statement as follows:
The best estimate of the five is 6,000.
The green wedge, which represents Hall, is about 45% of the circle. The three wedges representing independents Carson, Franklin, and Lamont - dark red, bright red, and turquoise, respectively - together comprise about 40% of the circle. We can set up, and solve for the unknown in, a proportion statement as follows:
The best estimate of the five is 6,000.
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The above graph represents the results of a general election for two seats on the city council of Lincoln City. Frankllin and Hall are Democrats; Johns and Lamont are Republicans; Carson is an independent.
6,219 people voted for Republicans. Which of the following is the best estimate for the number of people who voted for Democrats?
The above graph represents the results of a general election for two seats on the city council of Lincoln City. Frankllin and Hall are Democrats; Johns and Lamont are Republicans; Carson is an independent.
6,219 people voted for Republicans. Which of the following is the best estimate for the number of people who voted for Democrats?
The two wedges that represent the Democratic candidates - green (Hall) and dark red (Franklin) - together make up about 60% of the circle. The two wedges that represent the Republican candidates - purple (Johns) and blue (Lamont) - make up about 35% of the circle. We can estimate the number of people who voted for a Democrat using a proportion statement:
10,660 is the best estimate.
The two wedges that represent the Democratic candidates - green (Hall) and dark red (Franklin) - together make up about 60% of the circle. The two wedges that represent the Republican candidates - purple (Johns) and blue (Lamont) - make up about 35% of the circle. We can estimate the number of people who voted for a Democrat using a proportion statement:
10,660 is the best estimate.
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David's trip expenses are pictured in the above pie chart (numbers = % of his total expenses). If he spent $75 on taxis, how much did he spend on hotel and souvenirs combined?
David's trip expenses are pictured in the above pie chart (numbers = % of his total expenses). If he spent $75 on taxis, how much did he spend on hotel and souvenirs combined?
David spent $75 on taxis, which were 15% of his total expenses on the trip. He therefore spent 75(100/15) = $500 on the trip altogether. The hotel and souvenirs make up 35% + 5% = 40% of his total expenses. 40% of 500 is $200.
David spent $75 on taxis, which were 15% of his total expenses on the trip. He therefore spent 75(100/15) = $500 on the trip altogether. The hotel and souvenirs make up 35% + 5% = 40% of his total expenses. 40% of 500 is $200.
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If 
of a number is 
, what is 
of the number?
If
Let x be the number in question.
Then 2/3 * x = 18.
x = 18 * 3/2 = 27
Now find 1/9 of 27:
1/9 * 27 = 3
Let x be the number in question.
Then 2/3 * x = 18.
x = 18 * 3/2 = 27
Now find 1/9 of 27:
1/9 * 27 = 3
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Twenty-six students planned to contribute an equal amount to purchase a gift for their teacher. After 18 students had paid, they had collected $76.50. What is the total price of the gift?
Twenty-six students planned to contribute an equal amount to purchase a gift for their teacher. After 18 students had paid, they had collected $76.50. What is the total price of the gift?
If $76.50 had been collected after 18 students had paid, we can determine how much each student contributed:
$76.50/18 = $4.25 per student
Now we can multiply this by the total number of students (26) to get the full price of the gift:
26 x $4.25 = $110.50
If $76.50 had been collected after 18 students had paid, we can determine how much each student contributed:
$76.50/18 = $4.25 per student
Now we can multiply this by the total number of students (26) to get the full price of the gift:
26 x $4.25 = $110.50
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If 
of 
is 
, then what is 
of 
?
If
The first part of the problem tells us that x% of 20 is 50. We can model x% as x/100 or 0.01x. To find x% of 20, we can multiply 0.01x and 20. In other words, we can write the following equation:
(0.01x)(20) = 50
Divide both sides by 20.
0.01x = 2.5
Divide both sides by 0.01.
x = 250.
The question then asks us to find 20% of x. We can represent 20% as 0.2, and we know that x is 250. Therefore,
20% of 250 = 0.2(250) = 50.
The answer is 50.
The first part of the problem tells us that x% of 20 is 50. We can model x% as x/100 or 0.01x. To find x% of 20, we can multiply 0.01x and 20. In other words, we can write the following equation:
(0.01x)(20) = 50
Divide both sides by 20.
0.01x = 2.5
Divide both sides by 0.01.
x = 250.
The question then asks us to find 20% of x. We can represent 20% as 0.2, and we know that x is 250. Therefore,
20% of 250 = 0.2(250) = 50.
The answer is 50.
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30% of what number is 20?
Solve to the nearest hundredth.
30% of what number is 20?
Solve to the nearest hundredth.
This is a very basic form percentage question. This can be rewritten:
0.3 * x = 20
(Remember, the word "of" in a word problem indicates multiplication, while the word "is" indicates an equals sign).
Solve for x: x = 20 / 0.3 = 66.67
This is a very basic form percentage question. This can be rewritten:
0.3 * x = 20
(Remember, the word "of" in a word problem indicates multiplication, while the word "is" indicates an equals sign).
Solve for x: x = 20 / 0.3 = 66.67
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A toy is on sale for 43% off. Its sale price is $21.37. What is the full price?
A toy is on sale for 43% off. Its sale price is $21.37. What is the full price?
An algebraic expression for this item is:
An algebraic expression for this item is:
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A salesperson for a car dealership earns 16% commission on all sales. She has sold one vehicle this week, a $82,000 SUV on Tuesday, and today is Saturday. She would like to earn a total of $10,000 in commissions by week's end. At the very least, how much in sales must she accomplish today to meet her goal?
A salesperson for a car dealership earns 16% commission on all sales. She has sold one vehicle this week, a $82,000 SUV on Tuesday, and today is Saturday. She would like to earn a total of $10,000 in commissions by week's end. At the very least, how much in sales must she accomplish today to meet her goal?
The salesperson has already earned a commission of 16% of $82,000, which is equal to
.
This exceeds her goal for the week of $10,000, so she has already reached her goal.
The salesperson has already earned a commission of 16% of $82,000, which is equal to
This exceeds her goal for the week of $10,000, so she has already reached her goal.
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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?
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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A school is made up of 400 students. Each student must belong to one of the four clubs shown in the chart below. How many students are in chorus?
A school is made up of 400 students. Each student must belong to one of the four clubs shown in the chart below. How many students are in chorus?
You must first determine the percentage of the students in chorus. To do this, subtract the other percentages from 100: 100 – (35 + 29 + 24) = 12.
Therefore, 12% of the 400 students at this school attend chorus.
To determine the number of students in the chorus, multiply .12 (12%) by 400.
0.12(400) = 48
You must first determine the percentage of the students in chorus. To do this, subtract the other percentages from 100: 100 – (35 + 29 + 24) = 12.
Therefore, 12% of the 400 students at this school attend chorus.
To determine the number of students in the chorus, multiply .12 (12%) by 400.
0.12(400) = 48
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