Writing Systems of Equations from Word Problems

Trevor and Kylie are selling fruit for a school fundraiser. Customers can buy small boxes of oranges (x) and large boxes of oranges (y). Trevor sold 3 boxes of small oranges and 14 boxes of large oranges for a total of $203. Kylie sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220.

• $14x\ +\ 3y\ =\ 203$
  $11x\ +\ 11y\ =\ 220$
  

• $3x\ +\ 14y\ =\ 203$
  $11x\ +\ 11y\ =\ 220$
  

• $3x\ +\ 14y\ =\ 220$
  $11x\ +\ 11y\ =\ 203$
  

• $14x\ +\ 3y\ =\ 220$
  $11x\ +\ 11y\ =\ 203$
  

Eliezer's Ice-Cream Shop sells sundaes (x) for $2 and banana splits (y) for $3. On a hot summer day, he sold 8 more sundaes than banana splits and made $156.

• $x\ =\ y\ +\ 8$
  $3x\ +\ 2y\ =\ 156$
  

• $y\ =\ x+8$
  $2x\ +\ 3y\ =\ 156$
  

• $x\ =\ 8y$
  $2x\ +\ 3y\ =\ 156$
  

• $x\ =\ y\ +\ 8$
  $2x\ +\ 3y\ =\ 156$
  

Stacy went to the store to buy vegetables. The cost of 5 squash (x) and 2 zucchini (y) was $1.32. Three squash and 1 zucchini cost $0.75.

• $5x\ +\ 2y\ =\ 1.32$
  $3x\ +\ y\ =\ .75$
  

• $2x\ +\ 5y\ =\ 1.32$
  $x\ +\ 3y\ =\ .75$
  

• $5x\ +\ 2y\ =\ .75$
  $3x\ +\ y\ =\ 1.32$
  

• $2x\ +\ 5y\ =\ 1.32$
  $x\ +\ y\ =\ .75$
  

Alex decides to call for some fast food delivery. If he chooses McDonalds, the delivery fee is $7 and each sandwich costs $3.99. For KFC, there is no delivery fee but each sandwich (x) is $4.99. Let y be the total cost.

•  $3.99x\ +\ 4.99y\ =\ 7$  
   $x+\ y\ =\ 0$  
  

•  $y\ =\ 10.99x$  
   $y\ =\ 4.99x$  
  

•  $y\ =\ 4.99x\ +\ 7$  
   $y\ =\ 3.99x$  
  

•  $y\ =\ 3.99x\ +\ 7$  
   $y\ =\ 4.99x$  
  

A jar contains only nickels and quarters. The total number of coins in the jar is 15. The total value of the coins is $2.35. Which system of equations represents this situation?

• n + q = 2.35

  .05n + .25q = 15

• n + q = 15

  .5n + .25q = 15

• n + q =15

  .05n + .25q = 2.35

• .05n + q = 15

  n + .25q = 2.35

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.

• x + y = 33
  y = 2x - 3
• x + y = 33
  x = 2y - 3
• x + y = 33
  x = 3 - 2y
• x + y = 3
  x = 33 - 2y

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?

• x + y = 15
  4x + 2y = 44
• 4x + 2y = 15
  x + y = 44
• x = 2y + 44
  4x = y + 15
• 2x - 4y = 44
  x - y = 15

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?

• 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

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

• S + A = 530
  3S + 4A = 1740
• S + A = 530
  4S + 3A = 1740
• S + A = 1740
  3S + 4A = 530
• S + A = 1740
  4S + 3A = 530

Last season two running backs on the Steelers football team rushed a combined total of 1550 yards.  One rushed 4 times as many yards as the other.  Let x and y represent the number of yards each individual player rushed. 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