Multi Variable

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 steak for $17. If the total bill was $91, which system best represents the situation? Let "c" represent the # of people who ordered chicken and "s" represent those who ordered steak.

• c + s = 6
  14.80c + 17s = 91

• c + s = 91
  14.80c + 17s = 6

• c + s = 6
  14.80s + 17c = 91

• c + s = 91
  14.80s+ 17c = 6

Michael uses a blend of dark chocolate and milk chocolate to make the ice cream topping at his restaurant. He needs to buy 100 kg of chocolate in total for his next order. Dark chocolate costs $12 per kilogram, milk chocolate costs $10 per kilogram, and he wants to spend $1120 total. Let d be the number of kilograms of dark chocolate he buys and m be the number of kilograms of milk chocolate he buys. Which system of equations represents this situation?

• d + m = 100

  12d + 10m = 1120

• d + m = 1120

  12d + 10m = 100

• d + m = 100

  10d + 12m = 1120

• d + m = 1120

  10d + 12m = 100

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Writing Systems

Alexandra finds that she can give 5 haircuts and 3 hair dyes in 315 minutes. Giving 2 haircuts and 6 hair dyes takes 450 minutes.  Which system of equations represents the situation?

• 5x + 3y = 315

  2x + 6y = 450

• 3x + 6y = 450

  2x + 5y = 315

• 2x + 2y = 315

  3x + 5y = 450

• 3x + 5y =450

  2x + 6y = 315

A store in the Bolingbrook Promenade sells sweatshirts for $30 each and t-shirts for $12 each. You plan to spend $180 on t-shirts and sweatshirts. Which equation COULD model this situation?

• 180 + 12x + y = 30

• 12x + 30y = 180

• 30 + 12y = 180

• 30x + 12 = 180

Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total. Write a system to represent this situation assuming "a" represents # of adult tickets and "c" represents # of children's tickets. How many of each type of ticket were sold?

• x + y = 21

  6x + 4y = 104

• x + y = 104

  6x + 4y = 21

• x + y = 21

  6y + 4x = 104

• x + y = 104

  6x + 4y = 21

Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are twenty dollar bills and fifty dollar bills. How many of each bill does Caitlin have? Which system best represents the situation?

• x + y = 1430

  20x + 50y = 49

• x + y = 49

  10x + 5y = 1430

• x + y = 49

  20x + 50y = 1430

• x + y = 49

  x + y = 1430

Richardson Band is going to sell tickets to an outdoor performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used?

• 1s + 3c = 38

  2s + 3c = 52

• 3s + 1c = 38

  3s + 2c = 52

• s + c = 38

  s + c = 52

• 3s + 3c = 38

  1s + 2c = 52

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 steak for $17. Let x equal the number of chicken dinners and y equal the number of steak dinners. If the total bill was $91, which system best represents the situation?

• x + y = 6

  14.80x + 17y = 91

• x + y = 91

  14.80x + 17y = 6

• x + y = 6

  14.80y + 17x = 91

• x + y = 91

  14.80x+ 17y = 6

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.

• x + y = 33
  y = 2x - 3

• x + y = 33
  x = 2y - 3

Ben has 22 coins that total $3.10. If he only has nickels and quarters, which system of equations models best the situation?

• n + q = 22

  0.05n + 0.25q = 3.10

• n + q = 3.10

  0.05n + 0.25q = 22

• 0.05n + q = 22

  n + 0.25q = 3.10