Let's use the letter A to represent the number of adult tickets, and S to represent the number of student tickets.
We know that the total number of sold tickets was 175 (assuming everyone who bought a ticket went to the concert).
Thus, we can write:
[tex]A+S=175[/tex]
We also know that the number of sold adult tickets was 10 more than twice the number of student tickets. Thus, we have:
[tex]A=10+2S[/tex]
Now, notice that the first equation can be written as:
[tex]S=175-A[/tex]
Then, using the above result into the second equation, we obtain:
[tex]\begin{gathered} A=10+2(175-A) \\ \\ A=10+350-2A \\ \\ A+2A=360-2A+2A \\ \\ 3A=360 \\ \\ \frac{3A}{3}=\frac{360}{3} \\ \\ A=120 \end{gathered}[/tex]
Now, we can use the previous result to find S:
[tex]S=175-120=55[/tex]
Since we need to find how many more adults than students bought tickets, we need to subtract 55 from 120:
[tex]120-55=65[/tex]
Therefore, the answer is 65.
