Q: A recipe calls for a ratio of 3 cups of flour to 2 cups of sugar. If you want to use 8 cups of sugar, how many cups of flour should you use to keep the same ratio?

$$\frac{3}{2} = \frac{n}{8} \Rightarrow 3 \times 8 = 2 \times n \Rightarrow 24 = 2n \Rightarrow n = 12$$

Q: A chemist mixes a solution with a ratio of 5 parts water to 3 parts alcohol. If the chemist uses 45 mL of alcohol, how much water should be used?

$$\frac{5}{3} = \frac{n}{45} \Rightarrow 5 \times 45 = 3n \Rightarrow 225 = 3n \Rightarrow n = 75$$

Q: A school has 45 students absent, which is 6% of the total enrollment. What is the total number of students enrolled?

$$\frac{45}{n} = \frac{6}{100} \Rightarrow 45 \times 100 = 6n \Rightarrow 4500 = 6n \Rightarrow n = 750$$

Question 1

A hospital's patient count increased from 120 to 156 in one month. What is the percent of increase in the number of patients?

Accepted Answer

$$\frac{36}{120} \approx 0.3 = 30\%$$

Question 2

A medication bottle contains 250 mL. If a patient uses 60 mL, what percent of the bottle has been used?

Accepted Answer

$$\frac{60}{250} = 0.24 = 24\%$$

Question 3

A store marks down a jacket from $$80 to 60. $$What is the percent of decrease in price?

Accepted Answer

$$\frac{80-60}{80} = \frac{20}{80} = 0.25 = 25\%$$

Question 4

A recipe calls for a ratio of 3 cups of flour to 2 cups of sugar. If you want to use 8 cups of sugar, how many cups of flour should you use to keep the same ratio?

Accepted Answer

$$\frac{3}{2} = \frac{n}{8} \Rightarrow 3 	imes 8 = 2 	imes n \Rightarrow 24 = 2n \Rightarrow n = 12$$

Question 5

A chemist mixes a solution with a ratio of 5 parts water to 3 parts alcohol. If the chemist uses 45 mL of alcohol, how much water should be used?

Accepted Answer

$$\frac{5}{3} = \frac{n}{45} \Rightarrow 5 	imes 45 = 3n \Rightarrow 225 = 3n \Rightarrow n = 75$$

Question 6

A student scored 42 out of 56 on a test. What percent did the student score?

Accepted Answer

$$\frac{42}{56} = 0.75 = 75\%$$

Question 7

A car's value drops from $$25,000 to 20$$,000 over two years. What is the percent of decrease?

Accepted Answer

$$\frac{25,000 - 20,000}{25,000} = \frac{5,000}{25,000} = 0.2 = 20\%$$

Question 8

A nurse needs to prepare a solution that is 12% saline. If she needs 300 mL of solution, how many mL of saline should she use?

Accepted Answer

$$0.12 	imes 300 = 36 mL$$

Question 9

A city’s population increased from 80,000 to 100,000. What is the percent of increase?

Accepted Answer

$$\frac{100,000 - 80,000}{80,000} = \frac{20,000}{80,000} = 0.25 = 25\%$$

Question 10

A patient is prescribed a medication at a ratio of 2 mg per kg of body weight. If the patient weighs 75 kg, how many mg of medication should be administered?

Accepted Answer

$$2 	imes 75 = 150 mg$$

Question 11

A school has 45 students absent, which is 6% of the total enrollment. What is the total number of students enrolled?

Accepted Answer

$$\frac{45}{n} = \frac{6}{100} \Rightarrow 45 	imes 100 = 6n \Rightarrow 4500 = 6n \Rightarrow n = 750$$

Question 12

A laboratory technician needs to prepare a 40% alcohol solution. How much pure alcohol is needed to make 250 mL of this solution?

Accepted Answer

$$0.40 	imes 250 = 100 mL$$

Question 13

A company’s revenue increased from $$1,200,000 to 1$$,500,000. What is the percent of increase?

Accepted Answer

$$\frac{1,500,000 - 1,200,000}{1,200,000} = \frac{300,000}{1,200,000} = 0.25 = 25\%$$

Question 14

A nurse needs to dilute a medication in a 1:4 ratio (1 part medication to 4 parts water). If she has 20 mL of medication, how much water should she add?

Accepted Answer

$$\frac{1}{4} = \frac{20}{n} \Rightarrow 1 	imes n = 4 	imes 20 \Rightarrow n = 80$$

Question 15

A student wants to know what percent 18 is of 72. Which equation correctly represents this problem?

Accepted Answer

$$n 	imes 72 = 18$$

Question 16

A patient’s cholesterol level dropped from 240 mg/dL to 180 mg/dL after treatment. What is the percent of decrease?

Accepted Answer

$$\frac{240 - 180}{240} = \frac{60}{240} = 0.25 = 25\%$$

Question 17

A school has a student-to-teacher ratio of 18:1. If there are 630 students, how many teachers are there?

Accepted Answer

$$\frac{18}{1} = \frac{630}{n} \Rightarrow 18n = 630 \Rightarrow n = 35$$

Question 18

A $500 phone is on sale for 15% off. What is the sale price?

Accepted Answer

$$500 - (0.15 	imes 500) = 500 - 75 = 425$$

Question 19

A doctor prescribes a medication at a ratio of 7 mg per 2 kg of body weight. If a patient weighs 50 kg, how many mg of medication should be administered?

Accepted Answer

$$\frac{7}{2} = \frac{n}{50} \Rightarrow 7 	imes 50 = 2n \Rightarrow 350 = 2n \Rightarrow n = 175$$

Chapter 6 Study Guide: Ratio, Proportion, and Percent

Study Guide - Practice Questions

Study Guide - Flashcards