Question 1198673
<font color=black size=3>
x = first integer
y = second integer
z = third integer<ul><li>Fact 1: The sum of 3 integers is 314. </li><li>Fact 2: The sum of the first and second integers exceeds the third by 40. </li><li>Fact 3: The third integer is 26 less than the first.</li></ul>x+y+z = 314 from fact 1
x+y = z+40 from fact 2 
z = x-26 from fact 3


Plug z = x-26 into the first equation
Then solve for y
x+y+z = 314
x+y+x-26 = 314
2x+y = 340
y = -2x+340


Let's plug those y and z expressions into the second equation and solve for x.
x+y = z+40
x+(-2x+340) = x-26+40
-x+340 = x+14
-x-x = 14-340
-2x = -326
x = -326/(-2)
x = 163


Use that to find the second integer
y = -2x+340
y = -2*163+340
y = 14


Use that to find the third integer
z = x-26
z = 163-26
z = 137


<font color=red>Summary:
x = 163
y = 14
z = 137</font>


Check:<ul><li>x+y+z = 163+14+137 = 314 which verifies fact 1</li><li>x+y = 163+14 = 177 which is 40 larger than z = 137, since 137+40 = 177, confirming fact 2</li><li>137 is 26 less than 163 since 163-26 = 137, which confirms fact 3.</li></ul>
</font>