# 7th grade Party

### By: Abbigail Hooper

## Tables for food

## Point of intersection for food

## Food graph

## Questions

## Describe how you created each equation.

To create each equation I was obviously looking for y so that is what I started with. Now I have to find my roc which Is the amount per student in this case 9.25 or 10.00. I then put an x to have y=10.00x or y=9.25x and the x represents the number of people. When solving the equation x will become a number and multiplied by your roc. I then knew there was a setup fee so, I had to add that to the equation and put it where the b is which is your base fee. The base fee is the amount you pay the server for setting up. So in this case the base fee is 20.00 or 61.25. So when our equations are both set up they should look like y=10.00x+20.00 and y=9.25x+61.25.

## 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, there will. This is called the point of intersection, which is when the two companies cost the same. To set up the equation you put each equation next to each other and put an equal sign in between. We put the equal sign in between because your point of intersection is when both equations are qual. Our goal is to get x by itself and plug it in. To get x by itself you first start by subtracting an x, in this case 10.00x-9.25x+20=9.25x-9.25x+61.25 now after subtracting we are left with .75x+20=61.25. Now we are going to subtract 20 from both sides of the equal sign .75x+20-20=61.25-20. After subtraction we are left with .75x=41.25. To get x by itself e are dividing both sides by .75. We are now left with x=55. Now that we have found the number of students (x) will be the same price at 55 we now have to figure out the cost. So we plug 55 into our equation y=10(55)+20 and we get 570. So this means the prices will both be $570.00 at 55.

## 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?

To start off your answer will not be a fraction or a decimal because you can’t have half of a person, so we know our answer will be a whole. Now we are going to find how many people we can have at the party with a budget of 1000 for both places. We know 1000 is our whole so 1000 is now our y and now we plug in the amount per person which in this case will be 10.00 and 9.25. x is what we are trying to find so we just leave it at x. if there is a base fee in this case 61.25 and 20.00 we add that on and our equations should look something like this 1000=10x+20 or 1000=9.25x+61.25 and now we solve. To solve I will be using the burger bonanza equation. First you ill subtract 20 from 20 and 20 from 1000 to get the 20 out of the equation. You are no left with 980=10x. Now we are going to divide both sides by 10 to get x by itself and we should get 98=x. so this means only 98 kids can come.

## proposed plan

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## Tables for bounce houses

## Point of intersection for bounce houses

## Bounce House graph

## Questions

## Describe how you created each equation.

## 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, there will. This is called the point of intersection, which is when the two companies cost the same. To set up the equation you put each equation next to each other and put an equal sign in between. We put the equal sign in between because your point of intersection is when both equations are qual. Our goal is to get x by itself and plug it in. To get x by itself you first start by subtracting an x, in this case 75x-54x+84=54x-54x. Now after subtracting we are left with 21x+84. Now we are going to divide both sides by 21 to get x by itself and we should get We are now left with x=4.. Now that we have found the number of hours (x) will be the same price at 4 hours we now have to figure out the cost. So we plug 4 into our equation y=75(4) and we get 300. So this means the prices will both be $300.00 at 4 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?

To start off your answer will not be a fraction or a decimal because you can’t have half of a person, so we know our answer will be a whole. Now we are going to find how many people we can have at the party with a budget of 750 for both places. We know 750 is our whole so 750 is now our y and now we plug in the amount per hour which in this case will be 54 and 75. x is what we are trying to find so we just leave it at x. If there is a base fee in this case jumpin’ jacks is 84. we add that on and our equations which should look something like this 750=54x+84 or 750=75x and now we solve. To solve I will be using the hoppin’ around equation. All you need to do id divide both sides by 75 to get x by itself and you should get x=10. This means only 10 people can come to the dance.

Proposed plan: I think the party should last 2 hours so the times will be 10am-12am so the best buy for 2 hours would be hoppin’ around.