Systems of Equations Word Problems and Practice

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

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 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.

If each bracelet is the same price and each necklace is the same price, determine how much each necklace costs.

• $11

• $4

• $10

• $6

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

Gabby and Sydney bought some pens and pencils. Gabby bought 4 pens and 5 pencils for $6.71. Sydney bought 5 pens and 3 pencils for $7.12. Find the cost of each.

Select the two choices below that define your variables.

• x = the cost of a pen

• y = the cost of a pencil

• x = 9 pens

• y = 8 pencils

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50.   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

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, 11)
• (12, 9)
• (11, 10)
• (9, 12)

Tags

CCSS.8.EE.C.8C

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.

To solve, I graphed:

x + y = 21

6x + 4y = 104

I got an intersection point at (10,11). What does that mean in context of the problem?

• There are 10 adults and 11 children.

• There are 11 adults and 10 children.

• The adults are $10 and the children are $11.

• There are 104 adults and 21 children.

Tags

CCSS.8.EE.C.8C

Solve the system:

x + y = 19

y = 3x - 1

• (14, 5)

• (11, 8)

• (5, 14)

• (8, 11)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6