PSAT/NMSQT Prep 2022 - Eggert M.D., Strelka A. 2022

Percents
Ratios, proportions, and percents
Data analysis

LEARNING OBJECTIVE

After this lesson, you will be able to:

· Calculate percents

To answer a question like this:

Teachers surveyed their students at two different schools about their favorite classes to find out how many students favored math class. At the first school, they asked 512 students and of those, 12.5 percent responded favorably. At the second school, 24.8 percent of 625 students responded favorably. What percent of all the students surveyed responded favorably?

A. 15.4%

B. 19.3%

C. 25.4%

D. 31.9%

You need to know this:

To calculate percents, use this basic equation:

Alternatively, use this statement: [blank] percent of [blank] is [blank]. Translating from English into math, you get [blank]% × [blank] = [blank].

You need to do this:

· Plug in the values for any two parts of the formula and solve for the third.

· In some calculations, you may find it convenient to express percents as decimals. To do this, use the formula above but stop before you multiply by 100 percent at the end.

Explanation:

Use a variation of the three-part percent formula to answer this question: whole × percent = part, where the percent is expressed as a decimal.

First, find the number of students at each school who responded favorably using the formula. For the first school: 512 × 0.125 = 64. For the second school: 625 × 0.248 = 155. Next, find the total number of students who were surveyed at both schools, which was 512 + 625 = 1,137, and the total number who responded favorably, 64 + 155 = 219. Finally, find the percent of people who responded favorably by using the formula one more time:

Of all the students surveyed, about 19.3% responded favorably, making (B) the correct answer.

Try on Your Own

Directions: Take as much time as you need on these questions. Work carefully and methodically. There will be an opportunity for timed practice at the end of the chapter.

11. A company sells dolls for $20 each. It decides to offer a discount of 20 percent for a month to see how many new customers it can attract. How much will each doll sell for during the month of the discount?

A. $12

B.$14

C.$16

D. $18

For Q12, begin by figuring out what percent of the budget actually goes to lunch.

12. A high school’s Environment Club receives a certain amount of money from the school to host an all-day event. The club budgets 40 percent of the money for a guest speaker, 25 percent for educational materials, 20 percent to rent a hotel conference room, and the remainder for lunch. If the club plans to spend $225 on lunch for the participants, how much does it plan to spend on the guest speaker?

A. $375

B.$450

C.$525

D. $600

13. A bag of marbles contains 60 marbles that are either red, blue, or yellow. If there are 12 blue marbles, what percent of the bag is made of red and yellow marbles?

A. 50%

B.60%

C.70%

D. 80%

Questions 14 and 15 refer to the following information.

The following table shows the chemical makeup of one mole (a unit of measure commonly used in chemistry) of acetone and the approximate mass of a mole of each component element.

HINT: For Q14, use the percent formula. Which is the part and which is the whole?

14. Oxygen makes up what percent of the mass of 1 mole of acetone? Round your answer to the nearest whole percent

15. If a chemist starts with 1,800 grams of acetone and uses up 930 grams, approximately how many moles of carbon are left? Round your answer to the nearest whole mole