Solving value mixture problem using a linear equation

Question

At the city museum, child admission is $6.30 and adult admission is $9.50. On Wednesday 176 tickets were sold for a total sales of $1355.20. How many child tickets were sold that day?

Answer 1

Let number of child admission tickets=x and number of adult admission tickets =y

 

The total number of tickets is 176 so x + y=176.

 

We also know the total sales of the tickets= $1355.20. So the equation would be:

 

6.30x+9.50y=1355.20

 

Now we can use the first equation we made and set it equal to y.

 

x +y= 176 => y=176-x

 

now since we know y= 176-x we can substitute it into this equation: 6.30x+9.50y=1355.20

 

Now we have=>

 

6.30x+9.50(176-x)=1355.20

Solve for X

 

6.30x +1672- 9.5x=1355.20

 

-3.2x+1672=1355.20

-3.2x=-316.8

x=99 And since we said X=child admission tickets => There were 99 child admission tickets sold

Answer 2

C=6.3

A=8.5

 

You need two equations to solve this, the total number of tickets sold and the total cost.  Then combine the equations through elimination to solve for one variable.

 

C+A=176  [Total number of tickets sold]

6.30C+9.50A=1355.20 [Total cost of Tickets sold]

 

I would take the first equation and multiply it by negative 6.30 to eliminate the variable C.

 6.3C+9.5A=1355.2

-6.3C-6.3A=-1108  [Subtract converted equation from original second equation]

        3.2A=246.4    [Now solve for A]

             A=77

 

If A=77, C=99 [A+C=176]