AMC 8 2008 Problem 13

Mr. Harman needs to know the combined weight in pounds of three boxes he wants to mail. However, the only available scale is not accurate for weights less than $100$ pounds or more than $150$ pounds. So the boxes are weighed in pairs in every possible way. The results are $122$, $125$ and $127$ pounds. What is the combined weight in pounds of the three boxes? $\textbf{(A)}\ 160 \textbf{(B)}\ 170 \textbf{(C)}\ 187 \textbf{(D)}\ 195 \textbf{(E)}\ 354$