Question:
The sum of two numbers is 15. Four times the smaller number is 60 less than twice the larger number. What is the larger number?

Answer:
Let $y$ be the larger of the numbers.  Since the numbers sum to 15, the other number is $15-y$.   Since four times the smaller number is 60 less than twice the larger, we have: \begin{align*}
4(15-y)&=2y-60\quad\Rightarrow\\
60-4y&=2y-60\quad\Rightarrow\\
120&=6y\quad\Rightarrow\\
20&=y.
\end{align*} The larger number is $\boxed{20}$, which makes the smaller number -5. We can check that our answer is correct by plugging the values into the original problem. We get $-5+20=15$ and $4(-5)=2(20)-60$, which result in $15=15$ and $-20=-20$.