the sum of three integers is 220. The sum of the first and second integers exceeds the third by 94. The third integer is 55 less than the first. Find the three integers.

first ---- x

third ---- x-55
second ---- 220 - (x + x - 55) = 275- 2x

"The sum of the first and second integers exceeds the third by 94"
---> x + x-55 = 275-2x + 94
4x = 424
x = 106

first is 106
third is 51
second is 63

check:
sum = 106+51+63 = 220 , ok
1st + 2nd = 157
3rd = 63
is 157 > 63 by 94 ? YES

To find the three integers, we need to set up a system of equations based on the given information and then solve for the variables.

Let's assume the three integers are represented by variables a, b, and c, respectively.

Based on the given information, we can set up the following equations:

1) a + b + c = 220 (The sum of the three integers is 220)
2) a + b = c + 94 (The sum of the first and second integers exceeds the third by 94)
3) c = a - 55 (The third integer is 55 less than the first)

Now, let's solve for the variables using these equations:

We can substitute equation 3) into equation 2) to eliminate the variable c:

a + b = (a - 55) + 94
a + b = a + 39 (simplify)
b = 39

Now, substitute the value of b into equations 1) and 2):

a + 39 + c = 220
a + 39 + (a - 55) = 220
2a - 16 = 220
2a = 236
a = 118

c = a - 55
c = 118 - 55
c = 63

So, the three integers are:

a = 118
b = 39
c = 63

Therefore, the three integers are 118, 39, and 63.