Step 1 :Let $s$ be the number of student tickets and $a$ be the number of adult tickets. Then we have the following equations:
Step 2 :$7s + 10a = 2750$
Step 3 :$s + a = 500$
Step 4 :Rearrange the second equation to get $a = 500 - s$
Step 5 :Substitute this expression for $a$ into the first equation: $7s + 10(500 - s) = 2750$
Step 6 :Simplify the equation: $7s + 5000 - 10s = 2750$
Step 7 :Rearrange the equation: $-3s = -2250$
Step 8 :Divide by -3: $s = 750$
Step 9 :Substitute the value of $s$ back into the expression for $a$: $a = 500 - 750 = -250$
Step 10 :Since the number of adult tickets cannot be negative, there is an error in the problem statement or the given information is inconsistent.