Nursing Elites

1. John’s Gym charges its members according to the equation y = 40x, where x is the number of months and y represents the total cost to each customer after x months. Ralph’s Recreation Room charges its members according to the equation y = 45x. What relationship can be determined about the monthly cost to the members of each company?

• A. John’s monthly membership fee is equal to Ralph’s monthly membership fee.
• B. John’s monthly membership fee is more than Ralph’s monthly membership fee.
• C. John’s monthly membership fee is less than Ralph’s monthly membership fee.
• D. No relationship can be determined between the monthly membership fees.

Correct answer: C

Rationale: The equation y = 40x represents John's Gym charging $40 per month, while the equation y = 45x represents Ralph's Recreation Room charging $45 per month. Since $40 is less than $45, it can be concluded that John's Gym offers a lower monthly membership fee compared to Ralph's Recreation Room. Therefore, the correct answer is that John’s monthly membership fee is less than Ralph’s monthly membership fee. Choices A and B are incorrect because John's fee is not equal to or greater than Ralph's fee. Choice D is incorrect as there is a clear relationship indicating that John’s monthly membership fee is less than Ralph’s monthly membership fee.

2. Which of the following is the independent variable in the equation below? f(t)=4t+9

• A. f
• B. 9
• C. t
• D. 4

Correct answer: C

Rationale: The independent variable in a function is the variable that is being manipulated or changed to obtain different values. In the equation f(t) = 4t + 9, the variable 't' is the independent variable. It is the variable that the function f(t) depends on, and changing its value will result in different outputs for the function. The other choices, 'f', '9', and '4', are not the independent variable as they do not represent the variable that is being manipulated to determine the function's output.

3. Solve the system of equations. Equation 1: 2x + y = 0 Equation 2: x - 2y = 8

• A. (1.8, 3.6) and (-1.8, -3.6)
• B. (1.8, -3.6) and (-1.8, 3.6)
• C. (1.3, 2.6) and (-1.3, -2.6)
• D. (-1.3, 2.6) and (1.3, -2.6)

Correct answer: B

Rationale: From Equation 1: 2x + y = 0. Solve for y: y = -2x. Substitute y = -2x into Equation 2: x - 2(-2x) = 8. Simplify to x + 4x = 8, then 5x = 8, and x = 8 ÷ 5 = 1.6. Substitute x = 1.6 back into y = -2x to find y = -3.2. Therefore, one solution is (1.6, -3.2). To find the second solution, use -1.6 for x to get (-1.6, 3.2). Thus, the correct answer is B, representing the solutions (1.8, -3.6) and (-1.8, 3.6). Choices A, C, and D contain incorrect values that do not match the solutions derived from solving the system of equations.

4. Complete the following equation: 2 + (2)(2) - 2 ÷ 2 = ?

• A. 5
• B. 3
• C. 2
• D. 1

Correct answer: A

Rationale: To solve the equation, follow the order of operations (PEMDAS/BODMAS): Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). 1. Calculate inside the parentheses first: (2)(2) = 4. 2. Then, perform multiplication and division: 2 + 4 - 1 = 6 - 1 = 5. Therefore, the correct answer is 5. Choice B (3) is incorrect because multiplication is done before subtraction. Choices C (2) and D (1) are incorrect as they do not follow the correct order of operations to solve the equation.

5. Solve the following equation: 3(2y+50)−4y=500

• A. y = 125
• B. y = 175
• C. y = 150
• D. y = 200

Correct answer: B

Rationale: To solve the equation 3(2y+50)−4y=500, first distribute to get 6y+150−4y=500. Combining like terms results in 2𝑦 + 150 = 500. By subtracting 150 from both sides, we get 2y = 350. Dividing by 2 gives y = 175. Therefore, the correct answer is B. Choices A, C, and D are incorrect because they do not correctly follow the steps of distributing, combining like terms, and isolating the variable to solve for y.

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