AMC 12 2024a Problem 17

Integers $a$, $b$, and $c$ satisfy $ab + c = 100$, $bc + a = 87$, and $ca + b = 60$. What is $ab + bc + ca$?

$\textbf{(A) }212 \textbf{(B) }247 \textbf{(C) }258 \textbf{(D) }276 \textbf{(E) }284$