# Unit 10 Project by Blake Grubbs

**Part A – Grab Some Grub**

Note -

Two companies have worked with us in the past to provide food for students whenever we have a party day. Recently, however, the companies have come under new management. This means that their prices may have changed a bit since the last time we used them. I managed to get some flyers from them regarding their rates for large orders of food, but I haven’t had a chance to check them out. Take a look at these flyers, and see what you make of them.

**Pizza Palace**

**Burger Bonanza**

Equation: y=10x+20

Number of Burgers

Price

Y

X

0

$20

50

$520

100

$1,020

150

$1,520

200

$2,020

250

$2,520

Equation: y=9.25x+61.25

Number of Pizzas

Price

Y

X

0

$61.25

50

$523.75

100

$986.25

150

$1,448.75

200

$1,911.25

250

$2,373.75

** **** Graph**

**Part A – Grab some Grub**

**Critical Thinking Questions**

1. Describe how you created each equation.

I looked at the rate of change and made it the X and then I looked at how much was being added to it and made that the y-intercept.

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, there would be and you would have to do y1-y2 and x1-x2. 50, 520 100, 1,020 100-50=50 1,020-520=500 50/500=1/10 520=1/10(1,020)+b 520-102=418=b

Burger Bonanza=418

50,523.25 100,986.25 100-50=50 986.25-523.25=463 50/463 986.25=50/463(523.25)+b 986.25=56.5064794816 (523.25)+b 56.5064794816

Pizza Palace=929.7435205184

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?

Burger Bonanza=98 people

Pizza Palace=101

No you can’t have a decimal or fraction because you can’t get a fraction of a person.

**Proposed Plan: I think that you should go with Pizza Palace because it is cheaper past 48 Pizzas.**

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**Part B – Bounce house**

Note –

After looking at some safety protocols for the district, I have decided that an obstacle course would be the best choice for our outdoor activity. I have taken the liberty of collecting some flyers from two of the highest rated companies in the area. I believe they charge an hourly rate, but they did mention something about a security deposit when I talked with them. You might want to check the flyer over carefully when thinking about the cost. Hope your planning is going well.

**Hoppin’ Around**

**Jumpin’ Jack’s **

Equation: y=75x

Hours

Price

Y

X

0

$0

2

$150

4

$300

6

$450

8

$600

10

$750

Equation: y=54x+84

Hours

Price

Y

X

0

$84

2

$192

4

$300

6

$408

8

$516

10

$624

**Graph**

**Part B – Bounce house**

**Critical Thinking Questions**

1. Describe how you created each equation.

I used the Rate of Change that was given and put it as the x and used the prepaid amount as the y intercept.

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, there is a point where both companies cost the same and that is at 4 hours I determined this by looking at the table.

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?

Hoppin’ Around=10 hours

Jumpin’ Jacks=12 hours 20 minutes

You can have a decimal or fraction because you can turn hours into minutes.

**Proposed Plan: I think that we should go with Hoppin’ Around because we don’t have to pay in advance so if they mess up there’s no loss.**