The teacher asks Bill to calculate $a-b-c$, but Bill mistakenly calculates $a-(b-c)$ and gets an answer of 11. If the correct answer was 3, what is the value of $a-b$?
I notice that Bill's mistake was to use the wrong order of operations: he subtracted $c$ from $b$ first, instead of subtracting $b$ from $a$ first. This means that Bill's answer is actually equal to $a-b+c$, not $a-b-c$. So I can write an equation: $a-b+c=11$. I also know the correct answer, which is $a-b-c=3$. I can use these two equations to eliminate $c$ and solve for $a-b$. I add the two equations together, and I get $2(a-b)=14$. I divide both sides by 2, and I get $a-b=7$. 