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

If of is , then what is of ?

100

200

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.

30% of what number is 20?

Solve to the nearest hundredth.

66.67

0.67

1.5

150%

None of the other answers

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

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

$$ 37.49$

$$ 49.70$

$$ 30.56$

$$ 33.55$

None of the available answers

Explanation

An algebraic expression for this item is:

$(1-0.43)x=21.37$

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

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?

She has already met her goal.

Explanation

The salesperson has already earned a commission of 16% of $82,000, which is equal to

$$ 82,000 \times 0.16 = $13,120$ .

This exceeds her goal for the week of $10,000, so she has already reached her goal.

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?

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

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?

$175

$200

$225

$250

$40

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.

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