Formulating 3 Variable Equations

1. A linear system has no solution when the graphs of the equations are parallel.

• TRUE

• FALSE

2. What is the solution?

• (1, -1)

• (-1, 1)

• (0, -2)

• (2, 0)

3. Solve the system.

• (3, -2, 4)

• (2, -3, 1)

• (-3, 2, -1)

• Infinitely many solutions

4. Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all. Upon completing the job he counted out the coins and it came to $6.60. Which system of equations could be used to find the exact number of dimes and nickels?

• d + n = 6.60

  .10d + .05n = 80

• d + n = 80

  d + n = 6.60

• d + n = 80

  .10d + .05n = 6.60

• d + n = 80

  .05d + .10n = 6.60

5. One group of people purchased 10 hot dogs and 5 soft drinks at a cost of $80. A second group bought 7 hot dogs and 4 soft drinks at a cost of $59. What is the price of one hot dog and one soft drink?

• 10h + 5s = 80

  7h + 4s = 59

• 7h + 4s = 80

  10h + 5s = 59

• 10h + 7h = 80

  5s + 4s = 59

• 5h + 10s = 80

  4h + 7h = 59

6. A resort hotel has 200 rooms. The rooms with kitchen facilities rent for $100 per night, those without kitchen facilities rent for $80 per night. On a night when the hotel was completely occupied, revenues were $17,000. Write a system to determine how many of each kind of room the hotel has if x represents the rooms with a kitchen and y represents a room without a kitchen.

• x + y = 200

  100x + 80y = 17000

• x + y = 200

  x + y = 17000

• x + y = 17000

  100x + 80y = 200

• x + y = 200

  80x + 100y = 17000

7.  An MLB stadium sells three types of tickets. Reserved tickets are sold for $20 each, field level tickets are sold for $50 each, and box seat tickets are sold for $100 each. You purchase 10 total tickets for $370. You have twice as many reserved tickets as field level tickets. Set up the system using the variables

x: reserved

y: field-level

z: box seats

• $x+y+z=370$
  $20x+50y+z=100$
  $2x=y$
  

• 
  

  $x+y+z=10$
  $20x+50y+100z=370$
  $x=2y$
  

• $2x+y+z=370$
  $20x+50y+100z=2$
  $2z=x$
  

8.  A local grocery store makes a 9-pound mixture of trail mix. The trail mix contains raisins, sunflower seeds, and chocolate-covered peanuts. The raisins costs $2 per pound, sunflower seeds cost $1 per pound, and chocolate-covered peanuts cost $1.50 per pound. The total cost for the mixture is $14.50. The mixture contains twice as many raisins than sunflower seeds.  Set up the system of equations using the following:

x: raisins
y: sunflower seeds
z: chocolate-covered peanuts

•  $x+y+z=\text{14}.50$  
   $2x+y+1.50z=9$  
   $x=2y$  
  

•  $x+y+1.5z=9$  
   $2x+y+z=14.50$  
   $2x=y$  
  

• 
  

   $x+y+z=9$  
  

   $2x+y+1.50z=14.50$  
   $x=2y$  
  

9. You have 17 coins in your pocket. There are pennies, nickels and dimes and they are worth a total of $0.47. There are four times more pennies than nickels. Write a system to determine how many of each type of coin you have.

• p + n + d = 17

  0.01p + 0.05n + 0.10d = 0.47

  p = 4n

• p + n + d = 17

  0.01p + 0.05n + 0.10d = 0.47

  n = 4p

• p + n + d = 0.47

  0.01p + 0.05n + 0.10d = 17

  p = 4n

• p + n + d = 17

  0.1p + 0.5n + 0.10d = 0.47

  n = 4p

10. The school that Laura goes to is selling tickets to the annual talent show. On the first day of ticket sales the school sold 4 senior citizen tickets, 2 adult tickets and 5 child tickets for a total of $55. The school took in $67 on the second day by selling 7 senior citizen tickets, 2 adult tickets and 5 child tickets. On the third day the show earned $46 when they sold 2 senior citizen tickets, 4 adult tickets and 2 child tickets. What is the price each of one senior citizen ticket, one adult ticket and one child ticket?

(Hint: the set up for your equations is similar to #5)

• Adult: $12

  Child: $8

  Senior: $8

• Adult: $7

  Child: $4

  Senior: $5

• Adult: $7

  Child: $5

  Senior: $4

• Adult: $4

  Child: $7

  Senior: $5