Illustrative Math Algebra

At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. If a system of equations is written, which would be the correct representation of the 2 variables?

• t: # of tacos
  m: # of glasses of milk

• t: Cost of each taco
  m: Cost of each glass of milk

• t: total cost
  m: # of food items

• t: Cost of each glass of milk
  m: Cost of each taco

At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, t, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?

• t + n = 54
  t = 3n + 8

• t + n = 54
  n = 3t + 8

• t + n = 54
  t = 3n - 8

• t + n = 8
  t = 3n + 54

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?

• (35, 52)

• (18, 69)

• ( 52, 35) 

• (61, 26)

Two brothers went shopping at a back-to-school sale where all shirts and shorts were the same price. The younger brother spent $175 on 7 new shirts and 7 pairs of shorts. The older brother purchased 6 new shirts and 7 pairs of shorts and paid a total of $165. How much did one shirt cost?

• $5

• $10

• $15

• $20

What is the solution?

• (1, -1)

• (-1, 1)

• (0, -2)

• (2, 0)

Stacy sells art prints for $12 each. Her expenses are $2.50 per print, plus $38 for equipment. Which system of equations represents Stacy's revenues (money earned) and expenses?

• Revenue: y = 12 + 2.5x

  Expense: y = 38

• Revenue: y = 12 + 38x

  Expense: y = 38

• Revenue: y = 12x

  Expense: y = 2.5x + 38

• Revenue: y = 12x

  Expense: y = 2.5 + 38x

Is the graph linear, exponential or neither?

• Linear

• Exponential

• Neither

Simplify the expression.
(x⁵ )(x⁵)

• x¹⁰

• x²⁵

• x¹⁶

• x⁸

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

• y = 15(35)^x

• y = 15(1.35)^x

• y = 15(0.35)^x

• y = 35(1.15)^x

Identify the y-intercept (initial value) in the function f(x)=13(.27)^x

• (.27)^x
• .27
• 13
• 3.51