Systems of Equations

A theater is showing a ballet performance. Tickets are available for three levels in the performance hall. Lower level tickets cost $35, mezzanine tickets cost $25, and upper balcony tickets cost $15. For a certain performance the theater sold 5 times as many lower level tickets as balcony tickets. The theater sold $37,500 in tickets that performance. The money made from mezzanine tickets alone was 4 times the money made from balcony tickets.

• x + y + z = 37500

  y - 4 x = 0

  x - 5 y = 0

• 35x + 25y + 15z = 37500

  x - 5 z = 0

  25 y - 60 z = 0

• 35x + 25y + 15z=37500

  y - 4z=0

  x - 5y=0

• 35x + 25y + 15z=37500

  55 - y=0

  100y - 15z=0

Carlos wants to rent a car. For the particular car he wants, Gentle Rental charges $185 per week plus 25 cents per mile driven. Rental Giant charges a flat fee of $275 per week. What is the number of miles driven so that renting from Gentle Rental cost Carlos less than renting from Rental Giant?

• less than or equal to 360 miles.

• less than 360 miles.

• less than or equal to 115 miles.

• less than 1,840 miles.

Phillip is an avid video game player and movie watcher. He has a choice of belonging to a video club with a monthly fee of $12 and a $1 a day rental fee for any movie or game or he can be a nonmember and pay a $2.50 a day rental fee for any movie or game. Which of the following is a reasonable solution for the number of movies or video games Phillip must rent for the cost to be equal between membership and non-membership?

Mathematical Equivalence

ON

Solve the following systems of equations

2x + 3y = 246

x + 9y = 36

• (3,6)

• (21,6)

• (-4,21)

• All Real Numbers

• No Solution

The following system of equations is shown below.

2x + 3y = 4

x - y = -3

What is x+y?

Mathematical Equivalence

ON

A cheetah is located 100 yards away from an antelope. The cheetah begins running on a straight path toward the antelope at a constant speed of 30 yards per second. At the same time, the antelope begins running away from the cheetah at a constant speed of 25 yards per second. If both animals continue to run on a straight path at the same speeds, how many seconds will it take for the cheetah to catch up to the antelope?

Mathematical Equivalence

ON

The school band collected $2,892 for 480 tickets sold to their spring concert. Adult tickets were $8 each and student tickets were $5 each. How many adult tickets were sold?

Mathematical Equivalence

ON