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.
There were
_children and
_adults at the show.

Answer 1

If all were children, revenue would be 700*$7 = $4900. Revenue is actually $6400 -4900 = $1500 more than that. Each adult admission that replaces a child's admission adds $10 -7 = $3 to the revenue, so there must have been
  $1500/$3 = 500 . . . . adult admissions

There were 200 children at the show.
There were 500 adults at ths show.

Answer 2

Hello!

You can make two expressions based on what you know

let x stand for the amount of children
let y stand for the amount of adults

x + y = 700
7x + 10y = 6400

You can multiply the first equation by 10 to be able to use elimination

10x + 10y = 700
7x + 10y = 6400

Subtract the two equations from each other

3x = 600

Divide both sides by 3

x = 200

Put x into one of the original equations to get y

200 + y = 700

Subtract 200 from both sides

y = 500

The answers are 200 children and 500 adults

Hope this helps!