Writing Systems of Equations from Word Problems

Match the sentence with this equation:
 $x\ +\ y\ =\ 15$  

• The difference of two numbers is 15

• The sum of two numbers is 15

• The product of two numbers is 15

• The quotient of two numbers is 15

Match a sentence with this equation:
 $2B\ +\ 3F\ =\ 22.50$  

• Joe bought 2 burgers and 3 fries for $22.50

• Mary bought 3 burgers and 2 fries for 22.50

• Norman ate 2 burgers and gave away 3 fries in 22.50 minutes

• Ivy bought 2 burgers and 3 fries for 2.20

Match a sentence with this equation: $C\ =\ 7.50p\ +\ 3.00$  

• JB's Deli charges $ 0.75 for each pizza and $3.00 per topping

• Sally's Pizza  charges $3.00 per pizza with a $7.50 delivery fee

• Pizza Time charges $7.50 for each pizza and $.30 for the delivery fee

• Pizza Planet charges $7.50 per pizza with a $3.00 delivery fee

Match an equation with the sentence:

The width of a rectangle is six less than the length.

• $W\ +\ L\ =\ 6$

• $W\ =\ 6\ -\ L$

• $W\ =\ L\ -\ 6$

• $W\ =\ L\ +\ 6$

Match an equation with the sentence:

 A total of 17 cats and dogs went to the beach

•  $C\ +\ D\ =\ 17$ 

•  $C\ -\ D\ =\ 17$ 

•  $CD\ =\ 17$ 

•  $C\ +\ 17=\ D$ 

Match an equation with the sentence:

 The difference of two numbers is -5

•  $x\ +\ y\ =\ -5$ 

•  $xy\ =\ -5$ 

•  $x\ -\ 5\ =\ y$ 

•  $x\ -\ y\ =\ -5$ 

Match an equation with the sentence:

 12 situps and 7 leglifts takes Mrs. Weber 3 minutes.

•  $12S\ +\ 7L\ =\ 3$ 

•  $12S\ -\ 7L\ =\ 3$ 

•  $12S\ -\ 3\ =\ 7L$ 

•  $7L\ +\ 3\ =\ 12S$ 

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used?

• 1s + 3c = 38

  2s + 3c = 52

• 3s + 1c = 38

  3s + 2c = 52

• s + c = 38

  s + c = 52

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 (all) the coins and it came to $6.60. Which system of equations could be used to find the exact number of dimes and nickels? (Hint: How much are the coins worth?)

• d + n = 6.60

  .10d + .05n = 80

• d + n = 80

  d + n = 6.60

• d + n = 80

  .10d + .05n = 6.60

On Monday Joe bought 10 cups of Coffee and 5 Doughnuts for his office at the (total) 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. 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