How to find the whole from the part with percentage - SAT Math

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Question

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?

Answer

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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Question

If $\frac{2}{3}$ of a number is , what is $\frac{1}{9}$ of the number?

Answer

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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Question

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?

Answer

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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Question

If of is , then what is of ?

Answer

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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Question

30% of what number is 20?

Solve to the nearest hundredth.

Answer

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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Question

A toy is on sale for 43% off. Its sale price is $21.37. What is the full price?

Answer

An algebraic expression for this item is:

$(1-0.43)x=21.37$

$x=\frac{21.37}{1-0.43}=$ 37.49$

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Question

On the ride home from school, Jim notices that pecent of the cars he passes are yellow. Jim sees yellow cars. How many cars does Jim see that aren't yellow?

Answer

Let x represent the total number of cars Jim sees on the way home. If Jim sees 7 yellow cars and notices that 35% of all the cars he sees are yellow, then we can express this as

7/x = 35%, or

$\frac{7}{x}=\frac{35}{100}$

Using cross multiplication, we see that

Therefore, Jim sees 20 total cars on the way home. The question wants to know how many cars are NOT yellow. We can find that by subtracting the total number of cars from the number of yellow cars:

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Question

17 is 85% of what number?

Answer

In this case, 17 is part of a whole x. We are also given that 17 is 85% of x.

With this in mind, we can set up the following proportion.

$\frac{17}{x}=\frac{85}{100}$

To solve for x, cross multiply.

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Question

is of what number?

Answer

To solve this problem, we can set up a proportion and solve for our missing value using cross multiplication.

$\frac{3}{x} = \frac{60}{100}$

$x = \frac{300}{60} = 5$

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Question

$\pi^2$ is $\pi%$ of what number?

Answer

Don't let the pi throw you off on this question. We can set up a proportion to solve for the whole that we are looking for.

$\frac{\pi^2}{x} = \frac{\pi}{100}$

(Remember that any percentage can also be written as a fraction.)

Now we can solve for our unknown by using cross multiplication.

$100\pi^2 = \pi x$

$100\pi = x$

Therefore, $\pi^2$ is $\pi%$ of $100\pi$ .

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Question

is of what number?

Answer

We can set up a proportion to solve this problem. Remember that we can express percentages as fractions.

$\frac{3}{x} = \frac{70}{100}$

Now we can cross-multiply and solve for our unknown.

$x = \frac{300}{70} = \frac{30}{7}$

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Question

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?

Answer

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.

Compare your answer with the correct one above

Question

If $\frac{2}{3}$ of a number is , what is $\frac{1}{9}$ of the number?

Answer

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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Question

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?

Answer

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

Compare your answer with the correct one above

Question

If of is , then what is of ?

Answer

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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Question

30% of what number is 20?

Solve to the nearest hundredth.

Answer

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

Compare your answer with the correct one above

Question

A toy is on sale for 43% off. Its sale price is $21.37. What is the full price?

Answer

An algebraic expression for this item is:

$(1-0.43)x=21.37$

$x=\frac{21.37}{1-0.43}=$ 37.49$

Compare your answer with the correct one above

Question

On the ride home from school, Jim notices that pecent of the cars he passes are yellow. Jim sees yellow cars. How many cars does Jim see that aren't yellow?

Answer

Let x represent the total number of cars Jim sees on the way home. If Jim sees 7 yellow cars and notices that 35% of all the cars he sees are yellow, then we can express this as

7/x = 35%, or

$\frac{7}{x}=\frac{35}{100}$

Using cross multiplication, we see that

Therefore, Jim sees 20 total cars on the way home. The question wants to know how many cars are NOT yellow. We can find that by subtracting the total number of cars from the number of yellow cars:

Compare your answer with the correct one above

Question

17 is 85% of what number?

Answer

In this case, 17 is part of a whole x. We are also given that 17 is 85% of x.

With this in mind, we can set up the following proportion.

$\frac{17}{x}=\frac{85}{100}$

To solve for x, cross multiply.

Compare your answer with the correct one above

Question

is of what number?

Answer

To solve this problem, we can set up a proportion and solve for our missing value using cross multiplication.

$\frac{3}{x} = \frac{60}{100}$

$x = \frac{300}{60} = 5$

Compare your answer with the correct one above

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