Translating System of Equations Word Problems

Last season two cats in the neighborhood caught a combined total of 1550 mice. One caught 4 times as many mice as the other. Let x and y represent the number of mice each individual cat caught. Which system of equations could be used?

• x + y = 1550

  y = 4x

• x + y = 1550

  y = x + 4

• y - x = 1550

  y = 4x

• y = 1550 + x

  y = x + 4

Answer explanation

The correct system of equations is x + y = 1550 and y = 4x. These equations represent the given information that one cat caught 4 times as many mice as the other, and the total number of mice caught is 1550.

Tags

CCSS.8.EE.C.8C

A cat lover, Justin, is planning to build a new cat house. The carpenter says that if he pays $100 now, his monthly payments will be $25 and his total cost will be $600. Which equation can be used to determine how many months Justin will be paying for his cat house?

• 25x + 100 = 600

• 25x - 100 = 600 

• 600 - 100x = 25

• 600 + 25x = 100 

Answer explanation

The equation 25x + 100 = 600 can be used to determine how many months Justin will be paying for his cat house. This equation represents the monthly payments of $25 and the total cost of $600.

Tags

CCSS.HSA.CED.A.3

Catherine finds that she can groom 3 cats and dye 2 cats' fur in 315 minutes. Grooming 2 cats and dyeing 4 cats' fur takes 450 minutes. Which system of equations represents the situation?

• 3x + 2y = 315
  2x + 4y = 450

• 3x + 2y = 450
  2x + 4y = 315

• 2x + 2y = 315
  3x + 4y = 450

Answer explanation

The correct system of equations is 3x + 2y = 315 and 2x + 4y = 450. This represents the given situation accurately.

Tags

CCSS.HSA.CED.A.3

On Monday, Cat Lady bought 10 cans of cat food and 5 cat toys for her cats at the cost of $16.50. It turns out that the cat toys were more popular than the cat food. On Tuesday, she bought 5 cans of cat food and 10 cat toys for a total of $14.25. Which equations could be used to determine the cost of the cat food?

• 10f + 5t = 14.25
  5f + 10t = 16.50

• 10f + 5t = 16.50
  5f + 10t = 14.25

• f + t = 10
  5f + 10t = 16.50

• f + t = 5
  5f + 10t = 16.50

Answer explanation

The correct equations to determine the cost of the cat food are 10f + 5t = 16.50 and 5f + 10t = 14.25. These equations represent the quantities of cat food and cat toys purchased on Monday and Tuesday, respectively, and their respective costs.

Tags

CCSS.8.EE.C.8C

A cat named Caitlin found a bag full of fish! She has 49 fish in all. She counts 1430 scales. There are twenty scale fish and fifty scale fish. How many of each type of fish 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

Answer explanation

The correct choice is x + y = 49 and 20x + 50y = 1430 because it represents the situation where Caitlin has 49 fish and counts 1430 scales, with twenty scale fish and fifty scale fish.

Tags

CCSS.HSA.CED.A.3

At a local pet store, Carla purchased a cat toy and a cat bed that cost a total of $54, not including tax. If the price of the cat toy, t, is $8 more than 3 times the price of the cat bed, n, which system of linear equations could be used to determine the price of each item?

• t + n = 54
  t = 3n + 8

• t + n = 54
  n = 3t + 8

• t + n = 54
  t = 3n - 8

• t + n = 8
  t = 3n + 54

Answer explanation

The correct system of linear equations is t + n = 54 and t = 3n + 8. This equation represents the relationship between the prices of the cat toy (t) and the cat bed (n) as given in the question.

Tags

CCSS.HSA.CED.A.3

Whiskers is 3 years younger than twice Mittens' age. Their ages combined are 33 years. How old are Whiskers and Mittens. If x=Whiskers' age and y=Mittens' 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

Answer explanation

The correct choice is x + y = 33 and x = 2y - 3 because it accurately represents the given situation and satisfies the conditions.

Tags

CCSS.8.EE.C.8C

Tommy the cat is 4 years older than twice Kitty's age. The sum of Tommy and Kitty's age is 48. If x=Tommy's age and y = Kitty's age, which system describes the situation above?

• x + 2y = 48

  y + 4 = x

• x + y = 48

  x = 2y + 4

• x + y = 48

  y = 2x + 5

• x + 2y = 4

  x + 4 = y

Answer explanation

The correct system of equations that describes the situation is x + y = 48 and x = 2y + 4. These equations represent Tommy's age being 4 years older than twice Kitty's age, and the sum of their ages being 48.

Tags

CCSS.HSA.CED.A.3

Tomcat is 5 years older than three times Kitty's age. The total of their ages is 44 years. If x=Tomcat's age and y=Kitty's age, which system describes the situation above?

• x + y = 44

  x = 3y + 5

• x + y = 44

  y = 3x + 5

• x + y = 44

  x = 5y + 3

• x + y = 44

  y = 5x + 3

Answer explanation

Tomcat's age is represented by x and Kitty's age is represented by y. The correct system that describes the situation is x = 3y + 5. This equation represents Tomcat being 5 years older than three times Kitty's age.

Tags

CCSS.HSA.CED.A.3

At a local pet store, John bought a cat tree and a cat bed that cost a total of $64, not including tax. If the price of the cat tree, t, is $10 more than 2 times the price of the cat bed, n, which system of linear equations could be used to determine the price of each item?

• t + n = 64
  t = 2n + 10

• t + n = 64
  n = 2t + 10

• t + n = 64
  t = 2n - 10

• t + n = 10
  t = 2n + 64

Answer explanation

The correct system of linear equations to determine the price of each item is t + n = 64 and t = 2n + 10.

Tags

CCSS.HSA.CED.A.3