Translating Algebraic Equations and Word Problems

Translate this phrase into an algebraic expression.
24 more than the number of cats Kitty has. 
Use c to represent the number of cats Kitty has.

• 24c

• c - 24

• c + 24

• c/24

Answer explanation

The correct choice is 'c + 24' because the phrase '24 more than the number of cats Kitty has' can be translated as 'c + 24' in algebraic expression.

Tags

CCSS.6.EE.A.2A

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

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

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

Translate this phrase into an algebraic expression.
15 less than the number of cats Sam has. 
Use d to represent the number of cats Sam has.

• 15d

• d - 15

• d + 15

• d/15

Answer explanation

The phrase '15 less than the number of cats Sam has' can be translated as 'd - 15', where d represents the number of cats Sam has. This expression subtracts 15 from the number of cats Sam has, which matches the correct choice.

Tags

CCSS.6.EE.A.2A

At a local pet store, Mary purchased a cat tree and a cat bed that cost a total of $74, not including tax. If the price of the cat tree, t, is $12 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 = 74
  t = 2n + 12

• t + n = 74
  n = 2t + 12

• t + n = 74
  t = 2n - 12

• t + n = 12
  t = 2n + 74

Answer explanation

The correct system of linear equations is t + n = 74 and t = 2n + 12. This system represents the relationship between the prices of the cat tree and cat bed.

Tags

CCSS.HSA.CED.A.3

Translate the statement into an equation:
Five less than the number of cats in a room is 6

• n - 5 = 6

• 5 - n = 6

Answer explanation

To translate the statement into an equation, we use 'n' to represent the number of cats. Since it is 'five less than' the number of cats, we subtract 5 from 'n'. So, the equation is n - 5 = 6. This equation represents the given statement correctly.

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