Question

Question 1

Part A: Explain why x = 3 makes 4x − 1 ≤ 11 true but not 4x − 1 < 11. (5 points)

Part B: What value from the set {4, 5, 6, 7, 8} makes the equation 8x + 1 = 57 true? Show your work. (5 points)

Question 2
A theater company has raised $870.75 by selling 25 floor seat tickets. Each ticket costs the same.

Part A: Write an equation with a variable that can be solved to correctly find the price of each ticket. Explain how you created this equation. (5 points)

Part B: Solve your equation in Part A to find the price of each floor seat ticket. How do you know your solution is correct? (5 points)

Question 3
A boating company has the following notice at the gate:

"Children under the age of 13 are not allowed to operate a boat."

Part A: Write an inequality to show the age of children who are allowed to operate a boat. (5 points)

Part B: Describe in words how you can show the solution to this inequality on a number line. (5 points)

Question 4

Sue earns $6 an hour walking her neighbor's dog.

Part A: Create two variables and determine which is dependent and which is independent for this situation. (4 points)

Part B: List three ordered pairs to show the values of the two variables. (3 points)

Part C: Write an equation to represent the relationship between the two variables. (3 points)

Answer 1

Explanation:

For part A:it has to be equal because if x=3 and they’re talking about 4x, that 4*3=12 and 12-1=11

For part B:it is 7 because if c=7 and it is 8x, 8*7=56 and 56+1=57

For Question 2/part a: if each ticket costs the same, you could call the price of the ticket x. The equation can be x*25=$870.75 which means that you have to divide870.75 by 25 which would equal $34.83 and you could plug $34.83 in x and solve the equation

For question 3: you could say:3 is not equal to 3+10 or 5 is not equal to 5+10

For question 4: I don’t know if this is right but I think that that price is dependent on the time because you won’t get the money if you don’t spend any time doing your job

Hope it helps!