Units 1-2 Cumulative Review Cumulus Cloud Re-Viewer

Units 1-2 Cumulative Review

Cumulus Cloud Re-Viewer ____________________________

1. Buster's Bouncy-House Boutique, which specializes in children's birthday parties, rents out its party rooms for a flat fee, plus a per-person charge for each attendee. Rather than just telling you how the charges are tallied, the manager quoted you a few hypothetical scenarios from the pricing structure for two of his more popular rooms: Moonwalk Mansion and Claustrophobia Cage.

Moonwalk Mansion

Claustrophobia Cage

a). What kind of relationship exists between number of attendees and price? How do you know?

Attendees 10 22

Price 350 410

Attendees 16 38

Price 248 424

b). Define variables and write equations for price in terms of number of attendees for both rooms.

c). What is the slope of the line describing the price for the Moonwalk Mansion? What does it mean in context?

d). What is the vertical intercept of the line describing the price for the Moonwalk Mansion? What does it mean in context?

e). Rewrite your equations describing price for each room. Then graph the equations on the grid below. Make sure you scale and label your axes appropriately. We want to see an intersection, if one exists. Moonwalk Mansion: Claustrophobia Cage:

f). Use the equations to find the number of attendees that would make the two rooms the same price.

g). How does this value relate to the graph? h). Use the graph to determine which room would be more expensive for a party with 80 attendees. Explain how you know.

2. When I was growing up, my family had a Christmas tradition. Each year, everyone would have oranges, walnuts, and quarters in his stocking. There was one fewer walnut than quarters. There were three times as many walnuts as oranges. There were three more quarters than oranges. Define variables, write equations, and determine how many oranges, walnuts, and quarters were in each person's stocking.

Solve the following system of equations both algebraically and graphically.

y 2x 32 1

2x y 11 0

Algebraically

Graphically

For the next problem, it will be helpful to know the following. Note that there are two "p"s. Capital P is Profit; lowercase p is price.

Revenue = (Price)(Number Sold) [R=p*x]

Profit = Revenue ? Cost

[P=R-C]

3. Raggs, LTD., a clothing firm, determines that in order to sell x suits, the price that they charge per suit must be

p 180 0.5x . It is also determined that the cost of producing x suits is modeled by C 3000 20x .

a) Write an equation to represent Revenue.

b) Write an equation to represent Profit.

c) How many suits should Raggs make to maximize profit?

d) What is the company's maximum profit?

e) What price is Raggs selling each suit for?

Algebra 1 and Arithmetic Review. Perform the indicated operations. A calculator should not be required.

1. 2x 52

2. 43x 22

3. 3x2 42x2 5x 3

4. 3x2 4 2x2 5x 3

5. 6 4(x 2)2

6 36 45 2

6.

25

Simplify. 4 3i

7. 2i

8. 3i 26

8 2i 9.

4 3i

Convert the following equations to standard form.

10. 3x 2 5x 12 2x 2 8x 6

11. 2x 32 5 x 2 3x 42

Factor

12. 54x6 250 y3

13. 64x 4 1

14. 4x 2 12x 9

Solve 15. 3x 2 5x 12 x 2 3x 3

16. 4x 2 9x 2x 15

17. 8 3x 22 152

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