SOLUTION: Adult tickets for a play cost $25 each and children's tickets cost $15 each. The total receipts were $7200 and the total attendance was 400. How many adults and how many children

Algebra ->  Expressions-with-variables -> SOLUTION: Adult tickets for a play cost $25 each and children's tickets cost $15 each. The total receipts were $7200 and the total attendance was 400. How many adults and how many children      Log On


   

Question 638539: Adult tickets for a play cost $25 each and children's tickets cost $15 each. The total receipts were $7200 and the total attendance was 400. How many adults and how many children attended?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of adult tickets sold
Let +c+ = number of children's tickets sold
given:
(1) +a+%2B+c+=+400+
(2) +25a+%2B+15c+=+7200+
----------------------
Multiply both sides of (1) by +15+
and subtract (1) from (2)
(2) +25a+%2B+15c+=+7200+
(1) +-15a+-+15c+=+-6000+
+10a++=+1200+
+a+=+120+
and, since
(1) +a+%2B+c+=+400+
(1) +120+%2B+c+=+400+
(1) +c+=+280+
120 adult tickets were sold
280 children's tickets were sold
check:
(2) +25%2A120+%2B+15%2A280+=+7200+
(2) +3000+%2B+4200+=+7200+
(2) +7200+=+7200+
OK