The sum of 3 integers is 194. the sum of the first and second integers exceeds the third by 80. The third integer is 45 less than the first. Find the three integers

Let

x = first integer

y = second integer

z = third integer

First equation: x + y + z = 194

Second equation: x + y = z + 80

Third equation: z = x - 45

Let's find the values of x, y and z.

Substitute 3rd eq to 1st eq:

x + y + x - 45 = 194

2x + y = 45 + 194

y = - 2x + 239

Plug in both we have solved for y and the 3rd eq to the 2nd eq to find x

x + (-2x + 239) = (x - 45) + 80

x - 2x - x = - 45 + 80 - 239

-2x = - 204

x = - 204/-2

x = 102

Solving for y,

y = - 2 (102) + 239

y = 35

Solving for z,

z = 102 - 45

z = 57