Ch 1.5 Solving Systems

Solve the system of equations: List the solution as a coordinate (x,y):

(a)  

Use elimination or substitution to solve the systems.

• (-2, -3, 3)

• (-2, 3, 3)

• (2, -3, 3)

A soccer team is ordering jerseys, shorts, and shoes. They have a budget of $1500 to spend on jerseys, x, that cost $15 each, shorts, y, that cost $20 each, and shoes, z, that cost $25 each. They want to buy 70 items in preparation for the upcoming season and they must order as many shoes as jerseys and shorts combined.

Write a system of three equations that directly models this situation.

• 1500

• z

• 70

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation? *

• 1.5x + 0.5y = 78.5
  x + y = 87
• 1.5x + 0.5y = 78.5
  1.5x + 0.5y = 87
• x + y = 78.5
  1.5x + 0.5y = 87
• x + y = 78.5
  x + y = 87

Tags

CCSS.HSA.CED.A.3

Kristin spent $202 on tops. Tank Tops cost $12, Graphic T- shirts cost $28 and Hoodies cost $35. She bought twice as many tank tops as hoodies. If she bought a total of 9 then how many of each kind did she buy?

• 4 tank tops, 3 graphic tees, and 2 hoodies

• 6 tank tops, 3 graphic tees, and 3 hoodies

• 2 tank tops, 6 graphic tees, and 1 hoodies

To find a solution by graphing is to find the point where two lines intersect.

• True
• False

Tags

CCSS.8.EE.C.8B

Write the system of inequalities
Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing.  

• x+y≤300
  7.5x+5.5y≥2000
• x+y<300
  7.5x+5.5y≥2000
• x+y≤300
  7.5x+5.5y≤2000
• x+y>2000
  7.5x+5.5y≤300

• (0,0)
• (6,2)
• (8,0)
• (0,6)

Which are vertices of the feasible region?

• (0, 3) (3, 0) (5, 8)

• (0, 6) (3, 5) (6, 5)

• (3, 3) (8, 5) (5, 8)

• (0, 5) (6, 0) (3, 3)

Tags

CCSS.HSA.REI.D.12

Objective quantity:
P = 30x + 50y
Corner that maximizes profit: (0, 6)
What is the profit?

• 300
• 280
• 400
• 240