SOLUTION: If 126 people attend a concert and tickets for adults cost $3 while tickets for children cost $2.25 and total receipts for the concert was $343.5, how many of each went to the conc

Algebra ->  Finance -> SOLUTION: If 126 people attend a concert and tickets for adults cost $3 while tickets for children cost $2.25 and total receipts for the concert was $343.5, how many of each went to the conc      Log On


   

Question 1034089: If 126 people attend a concert and tickets for adults cost $3 while tickets for children cost $2.25 and total receipts for the concert was $343.5, how many of each went to the concert?
Found 2 solutions by josmiceli, macston:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = number of adult tickets sold
+126+-+x+ = number of children's tickets sold
--------------------
+3x+%2B+2.25%2A%28+126+-+x+%29+=+343.5+
+3x+%2B+283.5+-+2.25x++=+343.5+
+.75x+=+60+
+x+=+80+
and
+126+-+80+=+46+
-------------------
80 adults and 46 children went to the concert
-------------------
check:
+3%2A80+%2B+2.25%2A%28+126+-+80+%29+=+343.5+
+240+%2B+103.5+=+343.5+
+343.5+=+343.5+
OK

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
A=adults; C=children
.
A+C=126
A=126-C . Use this to substitute for A below
.
3A+2.25C=343.5 . Substitute for A (from above)
.
3(126-C)+2.25C=343.5
378-3C+2.25C=343.5
-0.75C=-34.5
C=46
.
46 Children attended
.
A=126-C=126-46=80
.
80 Adults attended
.
CHECK:
.
3A+2.25C=343.5
3(80)+46(2.25)=343.5
240+103.5=343.5
343.5=343.5