The sum of three numbers is 61 the difference of the largest and the smallest is 50 and the sum of the two smaller numbers is 16 find the numbers

Let's say our numbers are x, y and z, where x>y>z.

x + y + z = 61

x - z = 50

y + z = 16

We can add those last two together and get

x + y = 66

We can put that into the first equation:

66 + z = 61

From here we get that z = - 5.

So:

x - (-5) = 50

x + 5 = 50

x = 45

We add this into the first:

45 + (-5) + y = 61

40 + y = 61

y = 21

Lets check:

45 - 5 + 21 = 61

45 - (-5) = 45 + 5 = 50

21 + (-5) = 21 - 5 = 16