Simons in Disguise

Integers $a$, $b$, and $c$ satisfy
\[
  ab+c=100,\qquad bc+a=87,\qquad ca+b=60.
\]
What is $ab+bc+ca$?
\[
  \textbf{(A)}\ 212 \qquad
  \textbf{(B)}\ 247 \qquad
  \textbf{(C)}\ 258 \qquad
  \textbf{(D)}\ 276 \qquad
  \textbf{(E)}\ 284
\]

Solutions

• Solution 1