Systems of equations
Two unknowns need two equations. Write one unknown in terms of the other, then substitute.
A worked example
250 tickets raise $2 100 at $10 and $6. With a adults, 10a + 6(250 − a) = 2 100, so 4a = 600 and a = 150.
The mistake people actually make
Check your answer satisfies BOTH equations, not just the one you solved.