There were 429 people at a play. Admission was $8 dollars each for adults and $4

Question

There were 429 people at a play. Admission was $8 dollars each for adults and $4.50 each for children. The total receipts were $2641. How man adults and how many children attended?
Where did I go wrong ???
Adult tickets: x
Adult cost per ticket: 8.00
total: 8.00x
childrens tickets: (429-x)
childs cost per ticket: 4.50
total: 4.50(429-x)
8.00x+4.50(429-x)=2641
8.00x+1930.5-4.50x=2641
3.50x+1930.5=2641
3.50x=710.50
x=203
adult tickets: 203
child's tickets: 4.50(428-203)= 1017
total=203+1017=1220
This answer does not appear to total up...can some one tell me where i went wrong please :) thanks!!

Explanation / Answer

this is where you went wrong
total=203+1017=1220 and child's tickets: 4.50(428-203)= 1017
It is 429 not 428
total=203+1017=1220 should be total=203+c=429
c is the number of children not the cost of the children's tickets
The two equations you need are
a=number of adults
c= number of children
a+c=429
8a+4.5c=2641

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