Solving System of Equations Applications

The difference of a and b is 3. The sum of the variables is 13. Find the numbers.

• a = 7
  b = 10

• a = 8
  b = 5

• a = 10
  b = 13

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

Josh is thinking of two numbers. Their sum is -10 and their difference is -2. Which system of equations represents the situation?

• x - y = -10
  x + y = -2

• x = -2
  y = 5

• x + y = -2
  x - y = -10

• x + y = -10
  x - y = -2

When we add two numbers, x, and y, we get 12. When we subtract the two numbers, we get 4. What are the two numbers?

• The numbers are 8 and 4.

• The numbers are 6 and 6.

• The numbers are 12 and 0.

• The numbers are 11 and 1.

Step 3) SOLVE the SYSTEM:

x + 2y = 10.25

x + 4y = 18.57

What is the cost for a soda (x) and a slice of pizza (y)?

• The cost of a soda is $1.75.

  The cost of a slice of pizza is $4.25.

• The cost of a soda is $4.25.

  The cost of a slice of pizza is $1.75.

• The cost of a soda is $10.25.

  The cost of a slice of pizza is $18.75.

Write TWO equations of the system Eden sold 11 packages of sugar cookies and 3 packages of oatmeal cookies for a total of $208. Danna sold 1 package of sugar cookies and 14 packages of oatmeal cookies for a total of $266. What is the cost of one package of sugar cookie dough (x) and one package of oatmeal cookie dough (y)?

• 11x + 3y = 208

  x + 14y = 266

• x + 3y = 208

  11x + 14y = 266

• x + y = 208

  x + y = 266

• 3x + 11y = 208

  14x + y = 266

Step 3) SOLVE the system

11x + 3y = 208

x + 14y = 266

What is the cost of one package of sugar cookies (x) and one package of oatmeal cookies (y)?

• One package of sugar cookie dough is $14.

  One package of oatmeal cookie dough is $18.

• One package of sugar cookie dough is $15.

  One package of oatmeal cookie dough is $17.

• One package of sugar cookie dough is $208.

  One package of oatmeal cookie dough is $266.

Step 1) Define the variables for the system:

At Sam’s pizza a soda and 2 slices of everything pizza cost $10.25.  At Two Cousin’s a soda and 4 slices of everything pizza cost $18.75.  What is the cost for a soda and a slice of pizza?

• x = # of sodas purchased

  y = # of slices of pizza purchased

• x = cost of a soda

  y = cost of a slice of pizza

• x = Sam's Pizza

  y = Two Cousin's

Step 2) WRITE 2 EQUATIONS for the SYSTEM:

At Sam’s pizza a soda and 2 slices of everything pizza cost $10.25.  At Two Cousin’s a soda and 4 slices of everything pizza cost $18.75.  What is the cost for a soda (x) and a slice of pizza (y)?

• x = 10.25

  y = 18.75

• x + 2y = 18.75

  x + 4y = 10.25

• y = 2x + 10.25

  y = 4x + 18.75

• x + 2y = 10.25

  x + 4y = 18.75

Step 1) Define the variables

Eden sold 11 packages of sugar cookies and 3 packages of oatmeal cookies for a total of $208.  Danna sold 1 package of sugar cookies and 14 packages of oatmeal cookies for a total of $266. 

What is the cost of one package of sugar cookie dough and one package of oatmeal cookie dough?

• x = # of packages of sugar cookie sold

  y = # of packages of oatmeal cookies sold

• x = cost of a package of sugar cookies

  y = cost of a package of oatmeal cookies

• x = amount of money Eden made fundraising

  y = amount of money Danna made fundraising

• x = # of cookies sold

  y = total amount of money earned