Elimination Word Problems

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.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.

What is the cost of a single hot dog?

• $0.50

• $1.00

• $1.50

• $0.75

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.HSA.CED.A.2

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.

Determine the cost of each adult ticket and each children’s ticket.

• $3.00 for each adult ticket and $11.75 for each child ticket.

• $11.75 for each adult ticket and $3.00 for each child ticket.

• $6.00 for each adult ticket and $4.00 for each child ticket.

• $4.00 for each adult ticket and $6.00 for each child ticket.

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.2

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

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.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

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

Determine the cost of an orange and a banana.

• $0.75 for an orange and $0.50 for a banana

• $0.50 for an orange and $0.75 for a banana

• $0.25 for an orange and $1.00 for a banana

• $1.00 for an orange and $0.25 for a banana