which of the following describes a proportional relationship

ATI TEAS 7

TEAS Practice Math Test

1. Which of the following describes a proportional relationship?

A. Johnathan opens a savings account with an initial deposit of $150 and deposits $125 per month
B. Bruce pays his employees $12 per hour worked during the month of December, as well as a $250 bonus
C. Alvin pays $28 per month for his phone service plus $0.07 for each long-distance minute used
D. Kevin drives 65 miles per hour

Correct answer: A

Rationale: A proportional relationship is one in which two quantities vary directly with each other. In choice A, the amount deposited per month is directly proportional to the initial deposit. The relationship can be represented as y = 125x + 150, where x is the number of months and y is the total amount in the account. Choices B and C involve additional fixed amounts or variable costs that do not maintain a constant ratio, making them non-proportional relationships. Choice D refers to a constant speed of driving, which is not a proportional relationship as it does not involve varying quantities that change in direct proportion.

2. Margery plans a vacation with costs for airfare, hotel (5 nights), sightseeing, and meals. If she receives a 10% discount on additional hotel nights, what will she spend?

A. 1328.35
B. 1373.5
C. 1381.4
D. 1417.6

Correct answer: A

Rationale: To calculate Margery's total cost, we first need to find the cost without the discount. Let's say the original cost is x. With a 10% discount, she saves 10% of the cost of additional hotel nights. Since she is staying for 5 nights, the discount applies to 4 additional nights (5 - 1 night already included). Therefore, she saves 10% of 4 nights' cost. If x is the cost of 1 night, the total cost without discount is 5x. With the 10% discount, she saves 0.1 * 4x = 0.4x. So, the cost after discount is 5x - 0.4x = 4.6x. Given that the total cost is 5x for 5 nights, we can equate 5x to 4.6x to find x. Solving for x, we get x = Total cost / 5 = 5x / 5 = 4.6x / 5. Therefore, x = 4.6x / 5, which simplifies to x = 0.92 * 5x. This means 1 night's cost is 0.92 times the total cost for 5 nights. Given the total cost is $1328.35, we find the cost for 1 night is $1328.35 / 5 = $265.67. So, Margery will spend $1328.35 for her vacation.

3. A scientist is trying to determine how much poison will kill a rat the fastest. Which of the following statements is an example of an appropriate hypothesis?

A. Rats that are given lots of poison seem to die quickly.
B. Does the amount of poison affect how quickly the rat dies?
C. The more poison a rat is given, the quicker it will die.
D. Poison is fatal to rats.

Correct answer: C

Rationale: A valid hypothesis must be a testable statement that predicts a relationship between variables. Option C is the only statement that presents a clear cause-and-effect relationship between the amount of poison given and the time it takes for the rat to die. Option A is descriptive without predicting an outcome, option B is a question rather than a statement, and option D is a general fact about poison and rats, lacking a specific hypothesis for testing.

4. Simplify the following expression: (3)(-4) + (3)(4) - 1

A. -1
B. 1
C. 23
D. 24

Correct answer: A

Rationale: To solve the expression, first calculate the multiplication: (3)(-4) = -12 and (3)(4) = 12. Then, substitute the results back into the expression: (-12) + 12 - 1 = -1. Therefore, the correct answer is A. Choices B, C, and D are incorrect as they do not result from the correct calculations of the given expression.

5. What is the result of dividing 8 by 4?

A. 2
B. 4
C. 6
D. 8

Correct answer: A

Rationale: To find the result of dividing 8 by 4, we divide 8 by 4, which equals 2. Choice B (4) is incorrect because it is the divisor, not the result of the division. Choice C (6) is incorrect as it is not the correct quotient. Choice D (8) is incorrect as it is the dividend, not the result of the division.