Solving Equations and Systems of Equations

Solving systems of equations word problems

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Multiple Choice

Bell Ringer!!!

Naomi caught half as many fish as Jack. Together, they caught 18 fish. How many fish did Jack catch?

• 6

• 9

• 12

• 15

Question 1

If Jane has 36 coins totaling $3.00, and the coins are all nickels and quarters, how many of each coin does she have?

If Jane has 36 coins totaling $3.00, and the coins are all nickels and quarters, how many of each coin does she have?

• Write one equation about the number of coins she has

• Write the other equation about the dollar amount of the coins she has

Multiple Select

If Jane has 36 coins totaling $3.00, and the coins are all nickels and quarters, how many of each coin does she have?

Which equations can you set up for this problem? Select 2

• n+q=3.00

• n+q=36

• 0.05n+0.25q=36

• 0.5n+0.25q=3.00

• 0.05n+0.25q=3.00

Multiple Choice

Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are twenty dollar bills and fifty dollar bills. How many of each bill does Caitlin have? Which system best represents the situation?

• x + y = 1430

  20x + 50y = 49

• x + y = 49

  10x + 5y = 1430

• x + y = 49

  20x + 50y = 1430

• x + y = 49

  x + y = 1430

Multiple Choice

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the 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

• c + d = 5

  5c + 10d = 16.50

Multiple Choice

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

• 3s + 3c = 38

  1s + 2c = 52

Multiple Choice

Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total.

Solve the system:

a + c = 21

6a + 4c = 104

• # of adult tickets = 10

  # of child tickets = 11

• # of adult tickets = 12

  # of child tickets = 9

• # of adult tickets = 11

  # of child tickets = 10

• # of adult tickets = 9

  # of child tickets = 12

Multiple Choice

Amy sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Adam sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60. What is the price of 1 pack of sugar cookies and 1 pack of oatmeal cookies?

• Sugar Cookies $5

  Oatmeal Cookies $3

• Sugar Cookies $4

  Oatmeal Cookies $8

• Sugar Cookies $2

  Oatmeal Cookies $6

• Sugar Cookies $3

  Oatmeal Cookies $6

Open Ended

If Jane has 36 coins totaling $3.00, and the coins are all nickels and quarters, how many of each coin does she have?

Type how many coins of each she has. You may use any method to solve this system.

Here are the equations from the previous question

n+q=36

0.05n+0.25q=3.00

Open Ended

What equations can you write to solve this problem?

In a child’s bank are 11 coins that have a value of $1.85. The coins are either quarters and dimes. How many coins does each child have?