# Planning a Party!

## Introduction:

Mrs. Barker wants to have a 7th grade party. But she needs a little help organizing it. We need to make this party rock but also fit it in the budget. So come on, lets go!

## Food-Burger Bonanza:

Burger Bonanza Offers-

• Chicken, beef, turkey, and vegetarian burger
• Any choice of drink
• Regular, sweet potato fries, chips, or potato soup
• Pickle
• \$10 a person
• \$20 Catering Fee

## Food-Pizza Palace:

Pizza Palace Offers-

• 5 Different Variety of Pizza
• 3 Different Variety of Pasta
• Drink
• \$9.25 a person
• \$61.25 set up fee

## Critical Thinking Questions: Describe how you created each equation.

• Burger Bonanza: Well, to make a table you need an equation to help you figure out the total cost for the amount of people you want. So first every equation has the total cost (y=) Then you need to figure out the rate of change. So that would be \$10 per person (y=10x) the x represents the amount of people. Then there is a fee for \$20 and that would be the y-intercept. So the equation would be- y=10x+20.
• Pizza Palace- We need to take the same steps as before. You always start with the total cost (y=) Then we find the rate of change or cost per person. Which would be (y=9.25x). Next we find the y-intercept which is the fee of \$61.25. So our final equation is- y=9.25x+61.25

## Will there ever be a number of students where both of the companies cost the same?

Yes there will become a point where the companies will cost the same. I used an online graph which had a visual of the two lines and there point of intersection. Also if you plug in you x value in each equation you will come out with the same total cost.

• Burger Bonanza- y=10(55)+20 or (55*10)=550+20=\$570
• Pizza Palace- y=9.25(55)+61.25 or (9.25*55) 508.75+61.25=\$570

So if you have 55 students then both companies will have the same cost.

## If you have a budget of \$1000 for food how many students maxium would you be able to have?

Burgers Bonanza- You need the equation for this one. Since we know how much money we can spend, we can remove the y with 1000(1000=10x+20) To figure this out we need to plug in the x to make the total value be \$1000 or less than 1000. Lets use the number 98. So 1000=10(98)+20. That would be 98*10=980+20=\$1000. Only 98 students, exactly, can attend the party if you pay \$1000.

Pizza Palace- Again you need to use the equation to help us figure this problem. 1000=9.25x+61.25. Lets use the number 101. 1000=9.25(101)+61.25 That would be 9.25*101=934.25+61.25=\$995.50 Even though it does not equal \$1000 it doesn't go over the budget and it very close to 1000. So 101 students can attend at the party if you pay \$1000 and you will have \$4.50 leftover. Also the number of students can't be a fraction or a decimal because there is no "half" person there can only be whole numbers.

## Purpose Plan:

I believe Pizza Palace is the better deal for 55 students or more. Pizza Palace offers great food and is way better than burgers! If this party rocks, than more than 55 students are guaranteed to show up!

## Bounce House- Hoppin Around Offers:

• 12 Variety of bounce houses/obstacle course
• 100 sq. ft. bounce house
• 100 ft. long obstacle course
• \$75 per hour

## Bounce House- Jumpin Jacks Offers:

• 100 sq.ft. bounce house
• 100 ft. long obstacle course
• \$54 per hour
• \$84 fee

## Critical Thinking Questions: Describe how you created each equation.

Hoppin Around- To start the equation you always have a total amount of money spent which is the y value (y=) Then you want to find the rate of change or how much you pay per hour. (y=75x) The x value represents the hours and now we find the y intercept which is the fee. Since there is no y intercept our equation is y=75x.

Jumpin Jacks- Like I said before, you always have your total amount of money you spend (y=). Then you find the rate of change or how much you spend per hour. (y=54x) then you find the y-intercept or the fee. (y=54x+84) so our equation is y=54x+84

## Will there ever be a number of hours where both companies will cost the same?

Yes, there will be. As you saw in the table the 4th hour had a total of \$300. I knew this because if you plug in the same x value your y value will equal the same.

Hoppin Around- y=75(4)=300

Jumping Jacks- y=54(4)=216+84=300

## If you have \$750 how many hours can you have for the money your spending?

Hoppin Around- You need the equation to help you figure this problem out. We know the y value. (750=75x) We need to plug in the x to make it be the y value. So 75(10)= 750. So you can spend 10 hours on the bounce house for \$750.

Jumpin Jacks- We already have the y value. (750=54x+84) We need to find an x value where the y value equals 750 or less but close. Lets try 12. (750=54(12)+84 So 54*12=648+84= \$732. For Jumpin Jacks you can bounce for 12 hours and you save \$18!

You can not have half an hour because the question asked for hours only so that would only be whole numbers.

## Purpose Plan:

I believe hoppin around is the best choice. Even though Jumping jacks is the better deal for 12 hours, the party won't last that long. Hoppin around is the best choice if the party last for 4 hours or less.