SOE Word Problems

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

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used? 

• 1s + 3c = 38
  2s + 3c = 52
• 3s + 1c = 38
  3s + 2c = 52
• s + c = 38
  s + c = 52
• 3s + 3c = 38
  1s + 2c = 52

Tags

CCSS.HSA.CED.A.3

The equations

3s + 1c = 38

3s + 2c = 52

represent this situation:

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets.

What is the solution?

• 8 senior, 14, child

• 14 senior, 8 child

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50.  It turns out that the doughnuts were more popular than the coffee.  On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25.  Which equations could be used to determine the cost of the coffee? 

• 10c + 5d = 14.25
  5c + 10d = 16.50
• 10c + 5d = 16.50
  5c + 10d = 14.25
• c + d = 10
  5c + 10d = 16.50
• c + d = 5
  5c + 10d = 16.50

Tags

CCSS.8.EE.C.8C

10c + 5d = 16.50

5c + 10d = 14.25

Represents: On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50. It turns out that the doughnuts were more popular than the coffee. On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25. What is the solution?

• $1.25 per coffee, $0.80 per doughnut

• $0.80 per coffee, $1.25 per doughnut

Flagship Cinemas sells movie tickets that are $4 for matinees and $7 for regular. One night, the theater sells 578 tickets and collects $3365 in total ticket sales.
Which system best represents the situation?

• 4x + 7y = 578
  x + y = 3365
• 4x + 7y = 3365
  x + y = 578
• 4y + 7x = 578
  x + y = 3365
• 4y + 7x = 3365
  x + y = 578

Tags

CCSS.HSA.CED.A.3

4x + 7y = 3365

x + y = 578

Represents: Flagship Cinemas sells movie tickets that are $4 for matinees and $7 for regular. One night, the theater sells 578 tickets and collects $3365 in total ticket sales.

What is the solution?

• 227 matinees, 351 regular

• 351 matinees,227 regular

Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are twenty dollar bills and fifty dollar bills. How many of each bill does Caitlin have?  Which system best represents the situation? 

• x + y = 1430
  20x + 50y = 49
• x + y = 49
  10x + 5y = 1430 
• x + y = 49
  20x + 50y = 1430
• x + y = 49
  x + y = 1430

The SOE

x + y = 49

20x + 50y = 1430

represents the situation: Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are twenty dollar bills and fifty dollar bills. How many of each bill does Caitlin have?

• 34 twenties, 15 fifties

• 15 twenties, 34 fifties

There are 50 donkeys and chickens on a farm. There are a total of 174 legs. Which system below can be used to figure out how many of each animal the farm has? Use d to represent the number of donkeys. Use c to represent the number of chickens.

• d + c = 174

  4d + 2c = 50

• d + c = 50

  4d + 2c = 174

• d + c = 50

  2d + 4c = 174

• d + c = 174

  2d + 4c = 50

Tags

CCSS.8.EE.C.8C