Linear Applications and Simplifying Polynomials

The expenses for the homecoming dance were $1,800. The class members sold 279 tickets and made a profit of $3,450. Which equation could be used to find x, the price of each ticket sold?

• 279x + 1,800 = 3,450

• 1,800 − 279x = 3,450

• 279x − 1,800 = 3,450

• 1,800x + 279x = 3,450

Jamie’s Algebra  class is playing a game of Algebraic BINGO. To play the game, the teacher gives a table of values, a graph, or a verbal description representing a linear equation in two variables. Students must identify the linear equation and mark it on their BINGO cards.

The teacher gave the verbal representation "y is 8 more than 5 times a number.” Which is the correct answer for Jamie to mark on her BINGO card?

(a)  

Terri is starting a babysitting service to make some extra money. She plans to charge a base fee of $10plus $7 per hour.

What function can be used to find the total charge for Terri's babysitting service, y, based on the number of hours she babysits, x?

(a)  

Each month, Arnold receives $1,050 for working part-time at his uncle’s camera store. For each camera that he sells, he earns a $125 bonus. Which equation can be used to find Arnold’s total monthly paycheck, P(x), based on the number of cameras that he sells, x?

• 
  P(x) = 1,050x + 125

• P(x) = 125x + 1,050

• P(x) = 1/125x + 1,050

• 
  P(x) = 125x

The basketball booster club runs the concession stand during a weekend tournament. They sell hamburgers for $2.50 each and hot dogs for $1.50 each. They hope to earn $900 during the tournament.

 

Let x = the number of hamburgers sold and y = the number of hot dogs sold. Write an equation in standard form to represent the total amount the booster club wants to earn during the tournament.

Enter your answer in the box provided.

(a)  

Elisa bought some boxes of pencils for $3.99 each and some boxes of markers at $4.99 each. If p represents the number of boxes of pencils and m represents the number of boxes of markers, which equation describes the relationship between these two variables if she spent a total of $39.91 on these items?

(a)  

A student bought concert tickets online. The total cost, c, in dollars, of t tickets can be found using the function below.

c = 24.50t + 9.50

If the student spent a total of $83 on tickets, how many tickets did he buy?

(a)  

The perimeter of a rectangle is 42 centimeters. The length of the rectangle can be represented by (x + 4), and its width can be represented by (2x − 7). What are the dimensions of this rectangle in centimeters?

• Length = 10 and width = 11

• Length = 8 and width = 13

• Length = 6 and width = 15

• Length = 12 and width = 9

Matthew has a jar of 368 nickels and dimes he has been collecting. The total value of the coins is $28.40. 

Which system of linear equations and solution can be used to represent the number of nickels and dimes Matthew has in his collection?

• n + d = 368
  0.05n + 0.1d = 28.4
  168 nickels and 200 dimes

• n + d = 368
  0.01n + 0.05d = 28.4
  200 nickels and 168 dimes

• 
  n + d = 368
  0.05n + 0.1d = 28.4
  200 nickels and 168 dimes

• n + d = 368
  0.1n + 0.05d = 28.4
  168 nickels and 200 dimes

Kevin purchased fish at a grocery store.

• The fish cost $5 per pound for salmon and $3 per pound for catfish.

• He spent a total of $36.60 on the salmon and catfish. 

• He purchased a total of 10 pounds of salmon and catfish.

How many pounds of each type of fish did Kevin purchase?

• Salmon: 6.7 pounds
  Catfish: 3.3 pounds

• Salmon: 8.325 pounds
  Catfish: 1.675 pounds

• Salmon: 1.675 pounds
  Catfish: 8.325 pounds

• Salmon: 3.3 pounds
  Catfish: 6.7 pounds