### All PSAT Math Resources

## Example Questions

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

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:**

$200

$40

$175

$225

$250

**Correct answer:**

$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.

### Example Question #2 : Whole And Part

30% of what number is 20?

Solve to the nearest hundredth.

**Possible Answers:**

1.5

150%

66.67

None of the other answers

0.67

**Correct answer:**

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

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

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

**Correct answer:**

An algebraic expression for this item is:

### 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:**

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 #4 : How To Find The Whole From The Part With Percentage

If of is , then what is of ?

**Possible Answers:**

20

200

10

50

100

**Correct answer:**

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.

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

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

**Possible Answers:**

**Correct 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

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

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?

**Possible Answers:**

She has already met her goal.

**Correct answer:**

She has already met 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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