(Fermat 2024, Part B, Question 17, CEMC - UWaterloo)

Each of the variables $a$, $b$, $c$, $d$, and $e$ represents a positive integer with the properties that
$b+d \gt a+d$
$c+e \gt b+e$
$b+d=c$
$a+c=b+e$
Which of the variables has the greatest value?
$(A)$ $a$
$(B)$ $b$
$(C)$ $c$
$(D)$ $d$
$(E)$ $e$

Answer Submission Note(s)
Your answer should be a single capital letter, e.g. 'A'.