(3) Given 5 different real numbers, taking any two to find their sum yields 10 sum values, among which the smallest three sums are $32, 36, 37$, and the largest two sums are 48 and 51, then the largest number among these 5 numbers is equal to
(3) 27.5 Hint: Let these 5 numbers be $a<b<c<d<e$, then $a+b=32$, $a+c=36, c+e=48, d+e=51$, and it is shown below that $b+c=37$.
Since $c-b=4, d-c=3, d-b=7$, we have
$$
a+d=(a+b)+(d-b)=39,
$$

thus $b+c=37$. Therefore,
$$
2 a=(a+b)+(a+c)-(b+c)=31,
$$

so $a=15.5, b=16.5, c=20.5, e=27.5, d=23.5$, which means the largest number is 27.5.