At a movie theater the cashier sold 250 more adult tickets than children's
tickets. The adult's tickets were $6.00 each and the children's tickets were
$3.50 each. What is the least number of each type of ticket that the cashier
had to sell for the total receipts to be ATLEAST $2,750?

Let x = the number of children's tickets.

>>..the cashier sold 250 more adult tickets than children's tickets..<<

So the number of adult tickets was x + 250

>>..the children's tickets were $3.50 each..<<

So the receipts taken in from the x children's tickets was $3.50x

>>..The adult's tickets were $6.00 each..<<

So the receipts taken in from the x+250 adults' tickets was 6.00(x+250)

So the total receipts taken in from both was 3.50x + 6.00(x+250)

>>.. for the total receipts to be ATLEAST $2,750..<<

So we set 3.50x + 6.00(x+250) greater than or equal to 2750

      3.50x + 6.00(x+250) > 2750
      3.50 + 6.00x + 1500 > 2750
             9.50x + 1500 > 2750
                    9.50x > 1250
                        x > 1250/9.50
                        x > 131.5789474

So the least number of children's tickets was 132, and since
the number of adult tickets was x + 250, the least number of
adult tickets was 132+250 = 382.

Answer: at least 132 children's tickets and at least 382
adult's tickets.

Edwin