Applications Systems of Equations

Micah (x) and Mallory (y) worked together to reshelve the returned books at the library. Together, they reshelved 48 books. If Mallory reshelved one-third of the number of books that Micah reshelved. What is the system of equations that go with this scenario?

Erin (x) is 3 years younger than twice Alex's (y) 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

• x + y = 33
  x = 3 - 2y

• x + y = 3
  x = 33 - 2y

Erin (x) is 3 years younger than twice Alex's (y) age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, how old are Erin and Alex.

Mathematical Equivalence

ON

The athletic boosters sold a total of 10 T-shirts (x) and ball caps (y) at the Jacksboro football game. If each T-shirt was $10 and each ball cap was $5 how many shirts and caps did they sell if they made $65. Which system of equations goes with this scenario?

The athletic boosters sold a total of 10 T-shirts (x) and ball caps (y) at the Jacksboro football game. If each T-shirt was $10 and each ball cap was $5 how many shirts and caps did they sell if they made $65. How many T-shirts and ball caps did they sell?

• (3,7)

• (7,3)

• (9,1)

• (8,2)

Solve the system of equations with your preferred method.

• (4, 7)

• (3, 5)

• (6, 7)

• (5, 3)

Solve the system of equations with your preferred method:
y = -4x + 5
y =  3x - 16

• (-3, -25)

• (3,-7)

• (11, 17)

• (21, 47)

Jenna sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Maggie 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

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

• x + y = 33
  x = 3 - 2y

• x + y = 3
  x = 33 - 2y

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. 

• 35 nachos, 52 sodas

• 18 nachos, 69 sodas

• 52 nachos, 35 sodas

• 61 nachos, 26 sodas