Systems of Equations

You are running a concession stand at a basketball game. You are selling hot dogs and sodas.  Each hot dog costs $1.50 and each soda costs $0.50. At the end of the night you made a total of $78.50. You sold a total of 87 hot dogs and sodas combined. You must report the number of hot dogs sold and number of sodas sold. How many hot dogs were sold and how many sodas were sold?

First, create a systems of equations based

off of the underlined information.

 

1.5x + 0.5y = 78.50

x + y = 87

 

Using the substitution method,

solve the systems of equations.

 

y = 87 - x

1.5x + 0.5(87 - x) = 78.5

1.5x + 43.5 - 0.5x = 78.5

x + 43.5 = 78.5

x + 43.5 - 43.5 = 78.5 - 43.5

x = 35 hot dogs sold

 

 

y = 87 - 35

y = 52 sodas sold

 

 

Sydney was selling little trinkets by the shore.  She was selling stuffed animal squids, sharks and shell necklaces.  Each stuffed animal would  cost $5 and each necklace would cost $1.  At the end of the day, she made a total of $50.  She sold a total of 30 stuffed animals and necklaces combined.  How much stuffed animals did she sell? How many necklaces did she sell?

 

First create a systems of equations based 

off of the underlined informtation.

 

5x + y = 50

x + y = 30

 

Using the Elimination method, 

solve the systems of equations.

 

5x + y = 50

-(x + y = 30)

4x = 20

4x/4 = 20/4

x = 5 stuffed animals sold

 

5 + y = 30

5 - 5 + y = 30 - 5

y = 25 necklaces sold