Question

A movie Theater charges $6.50 for morning tickets and $8.75 for night tickets the theater sold 378 tickets for a total amount of $2929.50 how many morning tickets were sold

Answer 1

The number of sold morning tickets are 168.

Explanation:

Given,

Total number of tickets = 378

Total earned amount = $2929.50

Charge of each morning ticket = $6.50

Charge of each night ticket = $8.75

Solution,

Let the number of morning tickets be 'x'.

And also let the number of night tickets be 'y'.

So, the total number of tickets is the sum of number of morning tickets and number of evening tickets.

So, framing in equation form, we get;

`x+y=378\ \ \ \ equation\ 1`

Again, Total earned amount is the sum of number of morning tickets multiplied with charge of each ticket and number of evening tickets multiplied with charge of each ticket.

So, framing in equation form, we get;

`6.50x+8.75y=2929.50\ \ \ equation\ 2`

On multiplying equation 2 by 100 on both side, we get;

`100(6.50x+8.75y)=2929.50*100\\\\650x+875y=292950\ \ \ \ equation\ 3`

Now multiplying equation 1 by '650', we get;

`650(x+y)=378*650\\\\650x+650y=245700\ \ \ \ equation\ 4`

Now subtracting equation 4 from equation 3, we get;

`(650x+875y)-(650x+650y)=292950-245700\\\\650x+875y-650x-650y=47250\\\\225y=47250\\\\y=(47250)/(225)=210`

Now substituting the value of'y' in equation 1, we get;

`x+y=378\\\\x+210=378\\\\x=378-210=168`

Hence The number of sold morning tickets are 168.

Whereas The number of sold night tickets are 210.