Let x be the number of adult and let y be the number of children
5x + 3y = 823 --------------------------(1)
x + y = 243 ----------------------------(2)
We can now solve simultaneously
Multiply through equation (2) by 3
3x + 3y =729 -----------------(3)
subtract equation (3) from equation (1)
2x =94
Divide both-side of the equation by 2
x =47
substitute equationx = 47 into equation (2) and then solve for y
47 + y = 243
subtract 47 from both-side of the equation
y = 243 - 47
y = 196
Hence