Adult tickets for the school musical sold for $3.50 and student tickets sold for $2.50. Three hundred twenty-one tickets were sold altogether for $937.50. How many of each kind of ticket were sold.

SOLUTION : Let 'X' represent adult tickets

Let 'Y' represent student tickets

Now lets look at what we know about these two when thinking about them in money terms:

$3.50 per adult

$2.50 per student

Total made $937.50

Lets show it algebraically:

3.50x + 2.50y =$937.50

When thinking about the tickets in numbers we know the number of tickets sold were 321 so algebraically

x + y = 321

Two equations; two variables; we can solve...........

  x+ y = 321 ....... which is the same as.... y= 321 - x

3.50x + 2.50y = 937.50

Since y = 321-x, we can substitute this into second equation:

3.50x + 2.50(321-x)=937.50

3.50x+802.5-2.50x=937.50

3.50x-2.50x+802.5=937.50

1.00x+802.5=937.50

x=135

Then y=321-135

y=186

Check:

x+y =135+186= 321 check

3.50x+2.50y=3.50(135)+2.50(186)=472.50+465=937.50 check