The problem/questions are in the image below.

Hi there! :)

We can begin by writing algebraic equations to express both of the situations. Use the format y = mx + b (slope-intercept form) to display the cost of each:

Recall that:

m - rate of change of cost (ex: amount per guest)

b - initial charge (ex: cost to rent the room)

Write the equations given the information in the table:

Bowling-Fun: y = 4x + 250

Arcade-A-Rama: y = 9x + 120

Part A.

Solve for the number of guests that would result in a same price from both locations by setting the two equations equal to each other:

4x + 250 = 9x + 120

Begin solving by subtracting 4x from both sides:

250 = 5x + 120

Subtract 120 from both sides to further isolate x:

130 = 5x

Divide both sides by 5:

x = 26 guests.

Part B.

Find the less expensive choice by plugging in the amount of guests (80) for x:

Bowling-Fun: y = 4(80) + 250 = $570

Arcade-A-Rama: y = 9(80) + 120 = $840.

$570 < $840

Therefore, Bowling-Fun is the cheapest option for 80 guests.

Part C.

The slope represents the rate of change. In this instance, this is the amount per guest, which is $4 dollars.

Part D.

The y-intercept represents the initial, one-time amount. This is the amount paid for the room, which is $120.

both equations and proportions are better.