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

Study concepts, example questions & explanations for SAT Math

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Example Questions

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Example Question #1 : How To Find The Whole From The Part With Percentage

Sat_math_131_01

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?

Possible Answers:

$175

$225

$250

$40

$200

Correct answer:

$200

Explanation:

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.

Example Question #15 : Whole And Part

30% of what number is 20?

Solve to the nearest hundredth.

Possible Answers:

0.67

None of the other answers

150%

66.67

1.5

Correct answer:

66.67

Explanation:

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

Example Question #14 : Whole And Part

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

Possible Answers:

None of the available answers

\$ 30.56

\$ 49.70

\$ 33.55

\$ 37.49

Correct answer:

\$ 37.49

Explanation:

An algebraic expression for this item is:

(1-0.43)x=21.37

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

Example Question #3 : How To Find The Whole From The Part With Percentage

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?

Possible Answers:

Correct answer:

Explanation:

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

Example Question #15 : Whole And Part

If  of  is , then what is  of ?

Possible Answers:

10

20

50

100

200

Correct answer:

50

Explanation:

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.

Example Question #16 : Whole And Part

If  of a number is , what is  of the number?

Possible Answers:

Correct answer:

Explanation:

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

Example Question #17 : Whole And Part

17 is 85% of what number?

Possible Answers:

Correct answer:

Explanation:

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.

To solve for x, cross multiply.

Example Question #1 : How To Find The Whole From The Part With Percentage

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?

Possible Answers:

Correct answer:

Explanation:

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

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: 

 

Example Question #2 : How To Find The Whole From The Part With Percentage

 is  of what number? 

Possible Answers:

None of the given answers are correct. 

Correct answer:

Explanation:

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

Example Question #3 : How To Find The Whole From The Part With Percentage

 is  of what number? 

Possible Answers:

Correct answer:

Explanation:

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. 

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

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

Therefore,  is  of 

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