# 7th Grade Blowout!

## Equation

The equation for this problem is y=10x+20

## Table

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## Equation

The equation for this problem is y=9.25x+61.25

## Table

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## Critical Thinking Questions

1. Describe how you created each equation.

I knew the equation was y=mx+b. I knew that m was ten for Burger Bonanza and 9.25 for Pizza Palace. Now I have y=10x+b for Burger Bonanza and y=9.25x+b for Pizza Palace. I also know that b for Burger Bonanza is 20 and for Pizza Palace it is 61.25 so now I have y=10x+20 for Burger Bonanza and y=9.25x+61.25 for Pizza Palace.

2. 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. To do so, you take the two equations and put them on opposite sides of the equal sign and solve for x on both sides. You have 10x+20=9.25x+61.25. When you solve for x, you get 55. Now plug the x coordinate into either one of the equations and solve for y. This would be (10)55+20=(9.25)55+61.25. When solved, you get 570, the y-value. Now you have both the x and y coordinate points so you could know where the point of intersection is! For this problem, it would be (55,570).

3. 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?

You could have 98 people to the party for Burger Bonanza and 101 people for Pizza Palace. You cannot have a fraction or decimal because you can’t have only part of a person attending a party!

## Graph

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## My Plan!!!

My proposed plan varies depending on the number of students attend the party. If there are expected to be less than 55, then I suggest Burger Bonanza as the best company to go to. If you are planning on having over 55 students, then Pizza Palace would probably be the better option. If there are exactly 55 students coming to the party, then it doesn’t matter what company you choose from because the prices will be the same! (But everyone likes pizza better than burgers so if it comes down to it, then choose Pizza Palace!)

## Equation

The equation for this problem is y=54x+84

## Table

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## Equation

The equation for this problem is y=75x

## Table

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## Critical Thinking Questions

1. Describe how you created each equation.

I knew the equation was y=mx+b. I knew that m was 54 for Jumpin’ Jack’s and 75 for Hoppin’ Around. Now I have y=54x+b for Jumpin’ Jack’s and y=75x+b for Hoppin’ Around. I also know that b for Jumpin’ Jack’s is 84 and for Hoppin’ Around it is zero (because there isn’t a y-intercept) so now I have y=54x+84 for Jumpin’ Jack’s and y=75x for Hoppin’ Around.

2. 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.

Yes. To do so, you take the two equations and put them on opposite sides of the equal sign and solve for x on both sides. You have 54x+84=75x. When you solve for x, you get 4. Now plug the x coordinate into either one of the equations and solve for y. This would be (54)4+84=(75)4. When solved, you get 300, the y-value. Now you have both the x and y coordinate points so you could know where the point of intersection is! For this problem, it would be (4,300).

3. 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 could have a bounce house from Jumpin’ Jack’s for 12 and 1/3 hours (or 12.33333… hours or 12 hours and 20 minutes) and a bounce house from Hoppin’ Around for 10 hours. You can have a fraction or decimal as your answer because you can have part of an hour.

## Graph

(Click to enlarge)

## My Plan!!!

My proposed plan varies depending on the number of hours the bounce house would have to be rented for. If you wish to have it for anywhere less than four hours, then I suggest Hoppin’ Around as the better company to use. If you want the bounce house for any amount of time over four hours then would Jumpin’ Jack’s be the best company to buy from. If you want to rent it for exactly four hours, then it doesn’t matter which company you buy from because the price will be the same! (But if that’s true, pick the one that has the most fun bounce houses of the two!)