$7 for children and $10 for adults. 700 people attended, collected $6,400. How many children attended and how many adults attended?

Question

The admission fee for a charity event is $7 for children and $10 for adults. The event was attended by 700 people, and the total amount collected in admissions was $6,400. How many children attended and how many adults attended?

Answer 1

let a the number of adults and c is the number for children

then we have  a+c=700 (1) and 10a+7c=6400 (2) from the (1) we get c=700-a plugging this value to (2)

we get 10a+7(700-a)=6400 ---->> 10a+4900-7a=6400 and solving for a we get a=500 plugging this value to (1) we get 500+c=700 and solving for c we get c=200