Systems Word Problems

Your family goes to a restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14.80, and some order steak for $17. If the total bill was $91, which system best represents the situation? 

• x + y = 6
  14.80x + 17y = 91
• x + y = 91
  14.80x + 17y = 6
• x + y = 6
  14.80y + 17x = 91
• x + y = 91
  14.80x+ 17y = 6

Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all.  Upon completing the job he counted out the coins and it came to $6.60.  Which system of equations could be used to find the exact number of dimes and nickels? 

• d + n = 6.60
  .10d + .05n = 80
• d + n = 80
  d + n = 6.60
• d + n = 80
  .10d + .05n = 6.60
• d + n = 80
  .05d + .10n = 6.60

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

• (35, 52)
• (18, 69)
• ( 52, 35) 
• (61, 26)

In a pasture, there are horses and chickens. If there are a total of 28 animals and 80 legs, how many chickens and horses are there?

• 10 horses, 18 chickens
• 16 horses, 12 chickens
• 12 horses, 16 chickens
• 18 horses, 10 chickens

Two brothers went shopping at a back-to-school sale where all shirts and shorts were the same price. The younger brother spent $175 on 7 new shirts and 7 pairs of shorts. The older brother purchased 6 new shirts and 7 pairs of shorts and paid a total of $165. How much did one shirt cost?

• $5
• $10
• $15
• $20

9. A bowl contained 13 red and brown M&M’s. There was one more red M&M’s than brown M&M’s. How many of each color are in the bowl?

• RED 8

  BROWN 6

• RED 7

  BROWN 8

• RED 6

  BROWN 7

• RED 7

  BROWN 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.

•  $10x+5y=9.00$ 
    $7x+4y=12.50$  

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

•  $10x+5y=12.50$ 
    $7x+4y=9.00$  

•  $5x+10y=9.00$  
   $4x+7y=12.50$  

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.

• $12x+15y=132$
  $8x+11y=92$
  

• $12x+15y=92$
  $8x+11y=132$

• $15x+12y=132$
  $11x+8y=92$
  

• $15x+12y=92$
  $11x+8y=132$
  

• (2, -2)
• (2, 2)
• (-2, 2)
• (-2, -2)

How many solutions will this system have? 

• No solution
• One Solution
• I Don't Know
• Infinitely Many Solutions

Tags

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