Interpret Solutions to Systems

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

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

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. Define the variables in the system:

4x + 6y = 13

3x + 7y = 13.5

• x = number of apples

  y = number of bananas

• x = number of bananas

  y = number of apples

• x = price of one apple

  y = price of one banana

• x = price of one banana

  y = price of one apple

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

• S + A = 530

  3S + 4A = 1740

• S + A = 530

  4S + 3A = 1740

• S + A = 1740

  3S + 4A = 530

• S + A = 1740

  4S + 3A = 530

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, 68 sodas

• 52 nachos, 35 sodas

• 18 sodas, 68 nachos

Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. Define the variables in the system:

y = 9.65x + 43

y = 8.40x + 58

• x = price of one shirt

  y = price of order

• x = price of order

  y = price of one shirt

At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. If a system of equations is written, which would be the correct representation of the 2 variables? 

• t: # of tacos
  m: # of glasses of milk
• t: Cost of each taco
  m: Cost of each glass of milk
• t: total cost
  m: # of food items
• t: Cost of each glass of milk
  m: Cost of each taco

Tags

CCSS.8.EE.C.8C

In a pasture, there are horses and chickens. If there are a total of 28 animals and 80 legs, how many chickens and horses are there?

• 10 horses, 18 chickens
• 16 horses, 12 chickens
• 12 horses, 16 chickens
• 18 horses, 10 chickens

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

A local fish market is selling fish and lobsters by the pound. The fish costs $5.25 a pound, while the lobster costs $10.50 a pound. The fish market sells 28.5 pounds and makes $215.25?

• The market sold 16 pounds of fish and 12.5 pounds of lobster.
• The market sold 18 pounds of fish and 10.5 pounds of lobster.
• The market sold 12.5 pounds of fish and 16 pounds of lobster.
• The market sold 10.5 pounds of fish and 18 pounds of lobster.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

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. Solve the system:

x + y = 21

6x + 4y = 104

• 10 adult tickets, 11 child tickets

• 11 adult tickets, 10 child tickets

Two small pitchers and one large pitcher can hold 8 cups of water. One large pitcher minus one small pitcher holds 2 cups of water. How many cups of water can each pitcher hold?

• 8 large, 2 small

• 6 large, 2 small

• 4 large, 2 small

• 2 large, 2 small