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.