## Critical Thinking Questions

Describe how you created each equation

I created each equation by finding the rate of change and y-intercept and plugging them into the equation y=mx+b .

Will there ever be a number of students where both companies will cost the same? Describe the steps you would use and then solve for the number of students for which both companies will cost the same amount.

Yes, if 55 students are attending the cost will be the same. I figured this out by starting out with 10x+20=9.25x+41.25 . I then subtracted 9.25x from each side. After that, I divided each side by .75 and figured out that the point of intersection was 55. It would cost \$570.

If you only have a budget of \$1000 for food, how many people, maximum, would you be able to have at the 7th Grade Blowout for each company? Can you have a decimal or fraction as part of your answer? Why or why not?

For Pizza Palace you would only be able to have 101 students attend. For Burger Bonanza you would only be able to have 98 students attend. You cannot have a decimal because you have to have whole people.

## Proposed Plan:

If more than 55 students are attending Pizza Palace would be the cheaper place to order food, but if less than 55 students are attending Burger Bonanza would be the better choice. This is because the point of interception is 55. So, the cheaper option changes.

## Critical Thinking Questions

Describe how you created each equation

I created each equation by finding the rate of change and y-intercept and putting them into the equation y=mx+b.

Will there ever be a number of hours where both companies will cost the same? Describe the steps you would use and then solve for the number of hours for which both companies will cost the same amount.

The point of intersection is 300. I found this by looking at the graph and seeing that they intercept at 300. It would be four hours.

If you only have a budget of \$750 for the bounce house, how many hours, maximum, would you be able to have at the 7th Grade Blowout for each company? Can you have a decimal or fraction as part of your answer? Why or why not?

You can have a fraction because it is hours, and they can be split up. For Jumpin’ Jack’s you could rent it for 12.3repeating hours. For Hoppin’ Around you could have it for 10 hours.

## Proposed Plan:

If you are renting the bounce house for less than 4 hours Jumpin’ Jacks is best, but if you are renting it for more than 4 hours Hoppin’ around would be the cheaper option. This is because the point of intersection is 4 and the cheaper option changes.