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. Adrian measures the circumference of a circular picture frame with a radius of 3 inches. Which of the following is the best estimate for the circumference of the frame?

A. 12 inches
B. 16 inches
C. 18 inches
D. 24 inches

Correct answer: C

Rationale: To calculate the circumference of a circle, use the formula 2πr, where r is the radius. In this case, with a radius of 3 inches, the estimated circumference would be 2 x π x 3 = 6π ≈ 18.85 inches. Therefore, the best estimate for the circumference of the frame is 18 inches (Choice C). Choice A (12 inches) is too small as it corresponds to the diameter rather than the circumference. Choice B (16 inches) and Choice D (24 inches) are also incorrect as they do not reflect the accurate calculation based on the given radius.

3. Which statement about multiplication and division is true?

A. The product of the quotient and the dividend is the divisor.
B. The product of the dividend and the divisor is the quotient.
C. The product of the quotient and the divisor is the dividend.
D. None of the above.

Correct answer: C

Rationale: In division, the dividend is the number being divided, the divisor is the number you are dividing by, and the quotient is the result. Multiplying the quotient by the divisor gives the original dividend. This is the reverse of the division operation. Therefore, the correct statement is that the product of the quotient and the divisor equals the dividend, making option C correct. Choices A and B provide incorrect relationships between the terms dividend, divisor, quotient, and product, making them inaccurate. Option D is a general statement that does not provide the correct relationship between multiplication and division terms.

4. Which of the following is the y-intercept of the line whose equation is 7y − 42x + 7 = 0?

A. (1/6, 0)
B. (6, 0)
C. (0, −1)
D. (−1, 0)

Correct answer: C

Rationale: To find the y-intercept, set x = 0 in the equation 7y − 42x + 7 = 0. This simplifies to 7y - 42(0) + 7 = 0, which gives 7y = -7. Solving for y, we get y = -1. Therefore, the y-intercept is where x = 0, so the correct answer is (0, -1). Choice A (1/6, 0) is incorrect as it does not satisfy the given equation when x = 0. Choice B (6, 0) is incorrect as it represents the x-intercept. Choice D (-1, 0) is incorrect as it does not correspond to the y-intercept of the given equation.

5. What is the result of adding 1/6 and 1/2, expressed in reduced form?

A. 9/7
B. 1/3
C. 31/36
D. 3/5

Correct answer: B

Rationale: To add 1/6 and 1/2, you need a common denominator, which is 6. So, 1/6 + 3/6 = 4/6. Simplifying 4/6 gives 2/3, which is the correct answer (1/3). Choices A, C, and D are incorrect as they do not represent the correct sum of the fractions 1/6 and 1/2.