which of the following describes a real world situation that could be modeled by

ATI TEAS 7

TEAS Test Practice Math

1. Which of the following describes a real-world situation that could be modeled by?

A. Courtney charges a $12 fee plus $2 per hour to babysit. Kendra charges a $10 fee plus $5 per hour. Write an equation to find the number of hours for which the two charges are equal.
B. Courtney charges a $2 fee plus $12 per hour to babysit. Kendra charges a $5 fee plus $10 per hour. Write an equation to find the number of hours for which the two charges are equal.
C. Courtney charges a $12 fee plus $2 to babysit. Kendra charges a $10 fee plus $5 to babysit. Write an equation to find the number of hours for which the two charges are equal.
D. Courtney charges $10 plus $2 per hour to babysit. Kendra charges $12 plus $5 per hour. Write an equation to find the number of hours for which the two charges are equal.

Correct answer: A

Rationale: In the given situation, Courtney charges a $12 fee plus $2 per hour to babysit, represented by the equation: 12 + 2h where h is the number of hours. Kendra charges a $10 fee plus $5 per hour, represented by the equation: 10 + 5h. To find the number of hours for which the two charges are equal, we set the two equations equal to each other: 12 + 2h = 10 + 5h. Solving for h gives h = 2. This means that the charges are equal after 2 hours of babysitting. Choice B is incorrect because the fee and hourly rates for Courtney and Kendra are reversed, leading to an incorrect equation. Choices C and D are incorrect as they do not accurately represent the given scenario of fees and hourly rates for babysitting by Courtney and Kendra.

2. After a hurricane, donations were collected and divided into various categories. If 23% of the funds went towards construction costs, what is the percentage donated to support construction?

A. 0.49
B. 0.23
C. 0.18
D. 0.1

Correct answer: B

Rationale: The correct answer is B (0.23). To find the percentage of funds donated for construction costs, we need to consider the given percentage, which is 23%. In decimal form, 23% is represented as 0.23. Choices A, C, and D are incorrect because they do not match the correct decimal equivalent of 23%, which is 0.23. It's essential to convert percentages to decimal form accurately to calculate the correct percentage of funds allocated for a specific purpose.

3. University X requires some of its nursing students to take an exam before being admitted into the nursing program. In this year's class, half of the nursing students were required to take the exam, and three-fifths of those who took the exam passed. If this year's class has 200 students, how many students passed the exam?

A. 120
B. 100
C. 60
D. 50

Correct answer: C

Rationale: If the incoming class has 200 students, then half of those students were required to take the exam. (200)(1/2) = 100. So 100 students took the exam, but only three-fifths of that 100 passed the exam. (100)(3/5) = 60. Therefore, 60 students passed the exam. The correct answer is 60. Choice A is incorrect as it miscalculates the number of students who passed the exam. Choice B is incorrect as it does not consider the passing rate of the exam. Choice D is incorrect as it is much lower than the correct answer.

4. What is a common denominator?

A. A shared multiple of two denominators
B. A shared factor of two numerators
C. A number that is the same in all fractions
D. A number that divides evenly into both fractions

Correct answer: A

Rationale: A common denominator is a shared multiple of the denominators in a set of fractions. It is necessary when adding or subtracting fractions to have a common denominator to ensure that the fractions can be combined accurately. Choice B is incorrect because the common denominator is related to the denominators, not the numerators. Choice C is incorrect because while the common denominator is the same in all fractions being added or subtracted, it is not necessarily a number that is the same in all fractions. Choice D is incorrect because a common denominator is a multiple of the denominators, not a number that divides evenly into both fractions.

5. Dr. Lee observed that 30% of all his patients developed an infection after taking a certain antibiotic. He further noticed that 5% of those 30% required hospitalization to recover from the infection. What percentage of Dr. Lee's patients were hospitalized after taking the antibiotic?

A. 1.50%
B. 5%
C. 15%
D. 30%

Correct answer: C

Rationale: Out of all the patients who took the antibiotic, 30% developed an infection. Among those with infections, 5% required hospitalization. To find the percentage of all patients hospitalized, we multiply the two percentages: 30% * 5% = 1.5%. Therefore, 1.5% of all patients were hospitalized. Choice A (1.50%) is the calculated percentage of all patients hospitalized, not 1.50%. Choice B (5%) is the percentage of patients who developed an infection and required hospitalization, not all patients. Choice D (30%) represents the initial percentage of patients who developed an infection, not the percentage hospitalized.