Systems of Equations Word Problems

The difference of two numbers is 34 and their sum is 338.
Find the numbers.

The difference of two numbers is 34 and their sum is 338.
Find the numbers.

One number is 17 more than 3 times another number. The
sum of the two numbers is 41. Find the numbers.

​Now you try...

On the next slide select the correct equations that will solve this system.

Dropdown

One number is 17 more than 3 times another number. The sum of the two numbers is 41. Find the numbers.

One equation would be​​ ​

Select answer

​​ and the other equation would be​ ​

Select answer

​

Multiple Select

One number is 17 more than 3 times another number. The sum of the two numbers is 41. Find the numbers.

The two numbers are (choose both)...

• 35

• 6

• 20

• 21

• 30

Natalie has $84 more than Cierra. Together they have
$458. How much money do they each have?

Alyssa has $75 less than three times Eric. Together they
have $905. How much money do they each have?

​Let a=Alyssa and Let e=Eric

Open Ended

Alyssa has $75 less than three times Eric. Together they have $905. How much money do they each have?

What are the 2 equations you would use?

Jalen has $10.35 in Quarters and Nickels. He has a total of
99 coins. How many of each coin does he have?

Isaiah has $7.15 in Dimes and Nickels. He has a total of 91
coins. How many of each coin does he have?

​Set up the equations yourself and solve.

Lets use x for dimes and y for nickels.

Multiple Choice

Isaiah has $7.15 in Dimes and Nickels. He has a total of 91 coins. How many of each coin does he have?

Which of these is the solution to the system?

• 42 Dimes

  49 Nickels

• 52 Dimes

  39 Nickels

• 50 Dimes

  41 Nickels

• 48 Dimes

  43 Nickels

Three erasers and five pencils cost $7.55. 6 erasers and 12
pencils cost $17.40. How much does 1 eraser cost? How
much does 1 pencil cost?

Multiple Choice

Three erasers and five pencils cost $7.55. 6 erasers and 12 pencils cost $17.40. How much does 1 eraser cost? How much does 1 pencil cost?

Which is the correct solution to the system?

• Erasers = $.60

  Pencils = $1.15

• Erasers = $.70

  Pencils = $1.05

• Erasers = $.55

  Pencils = $1.20

• Erasers = $.50

  Pencils = $1.25

• Erasers = $.65

  Pencils = $1.10

17 apples and 12 oranges cost $10.44. 3 apples and 4
oranges cost $2.84. How much does 1 apple cost? How
much does 1 orange cost?

​Solve this one yourself and choose the correct answer on the next slide.

Multiple Choice

17 apples and 12 oranges cost $10.44. 3 apples and 4 oranges cost $2.84. How much does 1 apple cost? How much does 1 orange cost?

Which is the correct solution to the system?

• Apple = $0.30

  Orange= $0.47

• Apple = $0.28

  Orange= $0.49

• Apple = $0.20

  Orange= $0.57

• Apple = $0.24

  Orange= $0.53

• Apple = $0.23

  Orange= $0.54

The Odyssey Rockets Basketball team charges $5 for
adult tickets and $2 for student tickets. Last night made
$546 and sold 183 tickets. How many adult and student
tickets did they sell?

The local movie theater charges $13 for adult tickets and
$7 for children’s tickets. Yesterday they sold 115 tickets and
made $943. How many adult and children tickets did they
sell?

​Use the same method... you will fill in the blanks on the next 2 slides...

The width of a rectangle is 30 less than 4 times the length. The perimeter is 60. What is the length, width, and area of the rectangle?

The length of a rectangle is 15 more than 3 times the width. The perimeter is 110. What is the length and width?

​Choose the correct answer on the next slide

Multiple Choice

The length of a rectangle is 15 more than 3 times the width. The perimeter is 110.

What is the solution to the system?

• $$l=40\ w=15$$

• $$l=50\ w=5$$

• $$l=45\ w=10$$

• $$l=30\ w=25$$

• $$l=35\ w=20$$