System Word Problems (Standard Form)

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.

(Let c represent coffee and d represent doughnuts )

• 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.HSA.CED.A.2

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. Which system of equations represents the situation?

(Let x represent apples and y represent bananas)

• 4x + 6y = 3

  13.5x - 13y = 6

• x + y = 4

  x - y = 6

• 4x + 6y = 13

  3x + 7y = 13.5

• 4x - 6y = 13

  3x - 7y = 13.5

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2

There are 15 animals in a barn. These animals are horses and chickens. There are 44 legs in all. Which system of equations represents the situation?

(Let x represent horses and y represent chickens)

• x + y = 15

  4x + 2y = 44

• 4x + 2y = 15

  x + y = 44

• x = 2y + 44

  4x = y + 15

• 2x - 4y = 44

  x - y = 15

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2

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

(Let x represent children and y represent adults)

• 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

CCSS.HSA.CED.A.2

CCSS.HSA.REI.C.6

One group of friends purchased 10 hot dogs and 5 soft drinks at a cost of $12.50. A second group bought 7 hot dogs and 4 soft drinks at a cost of $9.00.

Let x = cost of hot dogs

Let y = cost of soft drinks

Write a system of linear equations.

•  $10x+5y=9.00$ 
    $7x+4y=12.50$  

•  $5x+10y=12.50$  
   $4x+7y\ =\ 9.00$  

•  $10x+5y=12.50$ 
    $7x+4y=9.00$  

•  $5x+10y=9.00$  
   $4x+7y=12.50$  

Tags

CCSS.8.EE.C.8C

At a local grocery store 5 oranges and 7 bananas cost $7.75, whereas 3 oranges and 9 bananas cost $8.25.

Let x = cost of oranges

Let y = cost of bananas

Write a system of linear equations.

• $7x+5y=8.25$
  $9x+3y=7.75$
  

• $7x+5y=7.75$
  $9x+3y=8.25$
  

• $5x+7y=7.75$
  $3x+9y=8.25$
  

• $5x+7y=8.25$
  $3x+9y=7.75$

Tags

CCSS.HSA.CED.A.3

The school that Nick goes to is selling tickets to their annual talent show. On the first day of ticket sales, they sold 12 adult tickets and 15 children tickets and made $132. On the second day of ticket sales, they sold 8 adult tickets and 11 children tickets for $92.

Let x = cost of adult tickets

Let y = cost of children tickets

Write a system of linear equations.

• $12x+15y=132$
  $8x+11y=92$
  

• $12x+15y=92$
  $8x+11y=132$

• $15x+12y=132$
  $11x+8y=92$
  

• $15x+12y=92$
  $11x+8y=132$
  

Tags

CCSS.8.EE.C.8C

Erik and Emily are shopping for gifts for their mothers. Erik bought one bracelet and 4 necklaces and spent $46. Emily bought 3 bracelets and 7 necklaces and spent $88.

Let x = cost of bracelets

Let y = cost of necklaces

Write a system of linear equations.

• $x+4y=88$
  $3x+7y=46$
  

• $x+4y=46$
  $3x+7y=88$
  

• $4x+y=46$
  $7y+3x=88$
  

• $4x+y=88$
  $7y+3y=46$

Tags

CCSS.HSA.CED.A.3

Erik bought one bracelet and 4 necklaces and spent $46.

Emily bought 3 bracelets and 7 necklaces and spent $88.

x+4y=46

3x+7y=88

What is the cost of a necklace (y) ?

Hint: Multiply the top equation by -3 to cancel the x terms.

• $4

• $6

• $10

• $9

Answer explanation

-3(x+4y=46)

-3x -12y = -138

3x+7y=88

Tags

CCSS.HSA.REI.C.6

CCSS.HSA.REI.C.5

Erik bought one bracelet and 4 necklaces and spent $46.

Emily bought 3 bracelets and 7 necklaces and spent $88.

x+4y=46

3x+7y=88

What is the cost of a bracelet (x) ?

Hint: Use your solution for y to solve for x.

• $4

• $6

• $3

• $8

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2

CCSS.HSA.REI.C.6