Alice has five real numbers $a < b < c < d < e$. She takes the sum of each pair of numbers and writes down the ten sums. The three smallest sums are $32$, $36$ and $37$, while the two largest sums are $48$ and $51$. Determine $e$.
Source: New Zealand NZMOC Camp Selection Problems 2017 p1
Tags: algebra
Alice has five real numbers $a < b < c < d < e$. She takes the sum of each pair of numbers and writes down the ten sums. The three smallest sums are $32$, $36$ and $37$, while the two largest sums are $48$ and $51$. Determine $e$.