Mid-unit 3 Review

Determine the Variables / Formulate the system of equations - Select the best two answers

The local college's bookstore sells collegiate t-shirts, hoodies and hats. During t their Family Visit Day Sale, the bookstore made a $119 Sale consisting of three t-shirts, a hoodie, and a hat: a $76 sale consisting of two t-shirts and two hats: and a $265 sale consisting of 5 t-shirts, 3 hoodies, and 2 hats. Calculate the price of each item.

• 3a + b + c = 119

  2a + 2c = 76

  5a + 3b + 2c = 265

• 3a + b + c = 76

  2a + 2c = 119

  5a + 3b + 2c = 265

• 3a + b + c = 265

  2a + 2c = 76

  5a + 3b + 2c = 119

• a = number of t-shirts

  b = number of hoodies

  c = number of hats

• a = Price of a t-shirt

  b = Price of a hoodie

  c = price of a hat

Solve using System of Equations

The local college's bookstore sells collegiate t-shirts, hoodies and hats. During t their Family Visit Day Sale, the bookstore made a $119 Sale consisting of three t-shirts, a hoodie, and a hat: a $76 sale consisting of two t-shirts and two hats: and a $265 sale consisting of 5 t-shirts, 3 hoodies, and 2 hats. Calculate the price of each item.

• a = 16

  b = 43

  c = 18

• a = 18

  b = 45

  c = 20

• a = 45

  b = 20

  c = 12

• a = 22

  b = 45

  c = 19

Determine the Variables / Formulate the Systems of equations / Choose the best two answers.

Raven has $80 in 15 bills in her pocket, including ones, tens, and twenties. If the number of one dollar bills is twice the combined number of tens and twenties, how many of each denomination does Raven have in her pocket

• x = number of one dollar bills

  y = number of ten dollar bills

  z = number of twenty dollar bills

• x = number of bills

  y = amount of money

  z = types of denominations

• x + y + z = 15

  x + 10y + 20z = 80

  x = 2(y +z)

• x + y + z = 15

  x + 10y + 20z = 80

  x = 4y + 2Z

• x + y + z = 15

  x + 5y + 10z = 90

  x = 2(y +z)

Solve using systems of equations

Input answer in order triple ex (7,8,9)

Raven has $80 in 15 bills in her pocket, including ones, tens, and twenties. If the number of one dollar bills is twice the combined number of tens and twenties, how many of each denomination does Raven have in her pocket

Solve the system of linear equations using algebraic methods.

a + b + c = 10

a - b - c = 4

a + b + 2c = 15

Solve the system of linear equations using algebraic methods.

x + y + z = 18

x - y + 2z = 25

5x - 20y -2z = 2

Solve the system of linear equations using algebraic methods.

r - 4s + 5t = 8

r + 2s - t = 2

r + s - 2t = 15

• r = -9

  s = -7

  t = -8

• r = 10

  s = 8

  t = 5

• r = 10

  s = -7

  t = -6

• r = -10

  s = -7

  t = 6

Solve the system of linear equations.

x + 2y - 3z = 9

x - y - z = 4

3x + 6y - 9z = 27

• No Solution

• x = 5

  y = -6

  z = 10

• x = 10

  y = 5

  z = -6

• Infinitely many solutions

x - y - z = 10

4x - 4y -4z = -8

x + y + 2z = 15

• Infinitely many solutions

• x = 4

  y = 6

  z= -2

• x = 8

  y = -4

  z = -3

• No solution