PC Advanced Systems and Applications

Christian had brochures printed for a new business venture. Christian originally ordered 4 boxes of black-and-white brochures and 3 boxes of color brochures, which cost a total of $134. After those ran out, Christian spent $120 on 3 boxes of black-and-white brochures and 3 boxes of color brochures. Which system represents this situation?

• x+y=134
  x+y=120
• 3x+3y=134
  4x+3y=120
• 4x+3y=134
  3x+3y=120
• 7xy=134
  6xy=120

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

There are 50 donkeys and chickens on a farm.  There are a total of 174 legs.  Which system below can be used to figure out how many of each animal the farm has?

• d + c = 174
  4d + 2c = 50
• d + c = 50
  4d + 2c = 174
• d + c = 50
  2d + 4c = 174
• d + c = 174
  2d + 4c = 50

Last season two running backs on the Steelers football team rushed a combined total of 1550 yards.  One rushed 4 times as many yards as the other.  Let x and y represent the number of yards each individual player rushed. Which system of equations could be used? 

• x + y = 1550
  y  = 4x
• x + y = 1550
  y = x + 4
• y - x = 1550
  y = 4x
• y = 1550 + x
  y = x + 4

You bought the meat for Saturday's cookout. A package of hot dogs costs $1.60 and a package of hamburgers costs $5. You bought a total of 8 packages of meat and you spent $23. Which system of equations represents this word problem?

• x - y = 8

  1.60x - 5y = 23

• x + 1.60x = 8

  y + 5y = 23

• x + 5y = 8

  1.60x + y = 23

• x + y = 8

  1.60x + 5y =23

Your family goes to a restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14.80 and some order the steak dinner for $17. If the total bill was $91, how many people ordered each type of dinner?

• 2 steak dinners

  4 chicken dinners

• 1 steak dinner

  5 chicken dinners

• 5 steak dinners

  1 chicken dinner

• 4 steak dinners

  2 chicken dinners

Click the two equations that you would use to answer the problem shown:

Find the value of two numbers if their sum is 16 and their difference is 2.

Rob has $1.65 in nickels and dimes. He has 25 coins in all. How many of each kind of coin does he have?

• 20 nickels

  5 dimes

• 17 nickels

  8 dimes

• 21 nickels

  4 dimes

• 8 nickels

  17 dimes

How would you know a system has no solution?

• You end up with 0=0 at some point.

• The value of one of the variables is 0 (i.e. x=0, y=0, or z=0).

• You end up with a false statement (e.g. 3=5) at some point.

• You end up with fractions at some point.

Say you wanted to eliminate x from the system shown. How would you do it?

• Add the equations without doing any multiplication.

• Multiply the first equation by 2 and the second equation by 3, then add the equations.

• Multiply the first equation by negative 2 and the second equation by 3, then add the equations.

• Multiply the first equation by 3 and the second equation by negative 2, then add the equations.