Question 1044739
.
Tickets are sold at $4.00 for adults and $2.50 for students. If 100 tickets were sold for $355.00, 
how many tickets were adult tickets? I need to define the variable, state the system and answer the question.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
Variables: let "x" be the numbers of adult tickets, and
           let "y" be the numbers of student tickets.

The system is:
 x +    y = 100,       (1)   ("100 tickets were sold") and
4x + 2.5y = 355.       (2)   ("100 tickets were sold for $355.00")

To solve the system, express "x" from (1): x = 100 - y, and substitute it into (2). You will get a single equation for y:

4*(100 - y) + 2.5y = 355.

Simplify and solve it:

400 - 4y + 2.5y = 355,   or

-1.5y = 355 - 400,

-1.5y = -45,

y = {{{(-45)/(-1.5)}}} = 30.

So, we just found y, the number of student tickets.

Then  x = 100 - y = 100 - 30 = 70. It is the number of adult tickets.

<U>Check</U>: 70*4 + 30*2.5 = 280 + 75 = 355.  Correct !

<U>Answer</U>.  70 adult and 30 student tickets were sold.
</pre>