System of Equation Word Problems from Tables

The country Buffet restaurant has tables that seat 6 people and booths that seat 4 people. The restaurant has 38 seating spaces to seat a total 188 people. Which system of equations could be used to find the number of tables, t, and the number of booths, b, that are at the restaurant?

Nancy went to the grocery story. On Monday she purchased 4 apples and 6 bananas for a total of $13. On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50. Which system of equations represents the situation?

• 4x + 6y = 3

  13.5x - 13y = 6

• x + y = 4

  x - y = 6

• 4x + 6y = 13

  3x + 7y = 13.5

• 4x - 6y = 13

  3x - 7y = 13.5

The seniors of Central High School and North High school are planning trips to Yellowstone National Park. Central filled 8 vans and 3 buses with 208 students. North filled 14 vans and 12 buses with 580 students. Each van and each bus carried the same number of students. Select the two equations you can use to determine how many students were in each van (v), and how many in each bus (b)?

• 14v + 12b = 580

• 8v + 3b = 208

• 8v + 12b = 208

• 12v + 14b = 580

• 3v + 8b = 208

Amy sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Adam sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60. What is the price of 1 pack of sugar cookies and 1 pack of oatmeal cookies?

• Sugar Cookies $5 
  Oatmeal Cookies $3

• Sugar Cookies $4
  Oatmeal Cookies $8

• Sugar Cookies $2
  Oatmeal Cookies $6

• Sugar Cookies $3
  Oatmeal Cookies $6

There were ​ (a)   students in each van and ​ (b)   students in each bus.

• 7

• 28

• 15

• 30

• 8

• 9

• 45

• 10

The table describes a system of two linear equatios. What is the solution of the system?

• (-2,3)

• (1,3)

• (3, 7)

• (4,9)

On the first night, the Movie House Theater sold 7 adult tickets and 11 child tickets for $227. On the second night they took in $150 by selling 6 adult tickets and 6 child tickets. Find the price of an adult ticket and the price of a child ticket.

• Adult $13
  Child $5

• Adult $10
  Child $6

• Adult $8
  Child $16

• Adult $12
  Child $13

Nancy went to the grocery story.  On Monday she purchased 4 apples and 6 bananas for a total of $13.  On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50.  Which system of equations represents the situation?

• 4x + 6y = 3
  13.5x - 13y = 6

• x + y = 4
  x - y = 6

• 4x + 6y = 13
  3x + 7y = 13.5

• 4x - 6y = 13
  3x - 7y = 13.5

Your family goes to Mississippi Fried for dinner. There are 6 people in your family. Some order the chicken fingers for $14.80, and some order the Deluxe Chicken Dinner for $17. 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