Non-linear equations (multi-variable)

The school that Braden goes to is selling tickets to a choral 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

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50. On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25.

Which system of equation best represents the scenario?

• 10c + 5d = 14.25

  5c + 10d = 16.50

• 10c + 5d = 16.50

  5c + 10d = 14.25

• c + d = 10

  5c + 10d = 16.50

• c + d = 5

  5c + 10d = 16.50

If trying to figure out how many $5 burritos and $3 tacos to buy, which equation represents the situation where you have $100 to spend?

SHOW ANSWER

• 100(B +T) = 8

• 3B = 100 + 5T

• 5B = 100 + 3T

• 5B + 3T = 100

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

Choose the system of linear equations that matches the word problem:

Excelerated Gym offers two plans. The first plan charges members a one time fee of $25 and a $10 per class fee. The second plan charges members $20 per class. Write a system to represent the two plans?

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

Choose the 2 numbers to complete the box

• 1

• 2

• 4

• 5

• 10

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