Applications of Linear Systems

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

• t + b = 38

  6t + 4b = 188

• 4t = 38

  6b = 188

• t + b = 188

  6t + 4b = 38

• t + b = 38

  4t + 6b = 188

Tags

CCSS.8.EE.C.8C

If the system of equations were:

t +b = 38 & 6t + 4b = 188 ,

what method should you use to solve?

• Graphing

• Substitution

• Elimination

• Pythagorean Theorem

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

The sum of Teresa’s and Cathy’s weight is 118 pounds. Teresa weighs 26 pounds more than Cathy. Which system of equations could you use to find Teresa’s weight, T and Cathy’s weight, C?

• T + C = 118

  T = 26

• T + C = 118

  T = C + 26

• T + C = 64

  T – C = 26

• T + C = 118

  C = T + 26

Tags

CCSS.HSA.CED.A.3

If the system of equations were:

T + C = 118 & T = C + 26,

what method should you use to solve?

• Graphing

• Substitution

• Elimination

• Vertical Line Test

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

The perimeter of a rectangular wood deck is 90 square feet. The deck’s length is 5 feet less than 4 times its width. Which system of equations could you use to find rectangle’s length, L and width, W?

• 2L + 2W = 90

  L = 5 – 4W

• 2L + 2W = 90

  L = 4W – 5

• L + W = 90

  L = 5W – 4

• L + W = 90

  W = 4L - 5

Tags

CCSS.8.EE.C.8C

An ice skating arena charges an admission fee for each child plus a rental fee for each pair of skates. John paid the admission fees for six nephews and rented five pairs of ice skates. He was charged $32. Juanita paid the admission fees for seven grandchildren and rented five pairs of ice skates. She was charged $35.25. Which system of equations could you use to find the amount of the admission fee, a and the ice skate rental fee, r?

• 32.00a + 5r = 5

  35.25a + 5r = 7

• 5a + 6r = 32.00

  5a + 7r = 35.25

• 8a + 5r = 32.0

  7a+ 7r = 35.25

• 6a + 5r = 32.00

  7a+ 5r = 35.25

Tags

CCSS.8.EE.C.8C

A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and Multiple Choice Questions worth 11 points each. This system of equations can be used to find how many of each type of question the test has:

x + y = 20

3x + 11y = 100

where , x represents the number of True/False questions and y represents the number of Multiple Choice questions. The solution to the system is (15 , 5). What is the correct interpretation of this solution?

• There are 5 multiple choice questions and 15 true/false questions.

• There are 15 multiple choice questions and 5 true/false questions.

• There are 100 multiple choice questions and 20 true/false questions.

• There are 15 multiple choice questions and 15 true/false questions.

Tags

CCSS.8.EE.C.8C

Monica buys 40 pieces of fruit. Each piece of fruit is either an apple or an orange. The number of apples totals 2 more than three times the number of oranges. Monica wrote the following system of equations where x represents the number of apples and y represents the number of oranges:

x + y = 40

x = 2 + 3y

The solution to the system is (30.5 , 9.5). Which statement below best describes the solution to the system of equations?

• There is no reasonable solution to this system of equations because the number of fruit cannot be negative.

• Monica has 30.5 apples and 9.5 oranges.

• There is no reasonable solution to this system of equations because the number of fruit cannot be fraction.

• Monica has 30.5 oranges and 9.5 apples.

Tags

CCSS.8.EE.C.8C

Monica buys 40 pieces of fruit. Each piece of fruit is either an apple or an orange. The cost of apples is $2 more than three times the cost of oranges. Monica wrote the following system of equations where x represents the cost of apples and y represents the cost of oranges:

x + y = 40

x = 2 + 3y

The solution to the system is (30.5 , 9.5). Which statement below best describes the solution to the system of equations?

• There is no reasonable solution to this system of equations because the number of fruit cannot be negative.

• The cost of an apple is $30.5 and the cost of an orange is $9.5.

• There is no reasonable solution to this system of equations because the number of fruit cannot be fraction.

• The cost of an apple is $30.50 and the cost of an orange is $9.50.

Tags

CCSS.8.EE.C.8C

The length of a rectangle is 2 less than six times its width. The perimeter of the rectangle is 88 cm. Find the dimensions of the rectangle. Which system of equations below could represent this situation?

• L = 2 - 6w

  L + w = 88

• L = 6w - 2

  L + w = 88

• L = 2 - 6w

  2L + 2w = 88

• L = 6w - 2

  2L + 2w = 88

Tags

CCSS.8.EE.C.8C