2013 AMC 10B Problems/Problem 3

Problem

On a particular January day, the high temperature in Lincoln, Nebraska, was 16 degrees higher than the low temperature, and the average of the high and the low temperatures was . In degrees, what was the low temperature in Lincoln that day?

$\textbf{(A)}\ -13 \qquad\textbf{(B)}\ \-8 \qquad\textbf{(C)}\ \-5 \qquad\textbf{(D)}\ \-3 \qquad\textbf{(E)}\ \111$ (Error compiling LaTeX. Unknown error_msg)

Solution

Let be the low temperature. The high temperature is . The average is . Solving for , we get