The sum of three integers is 211. The sum of the first and second integer exceeds the third by 39. The third interference is 23 less than the first. Find the three integers.

A= 109 B= 16 C=86

Step-by-step explanation:

Write an equation for each statement:

:

"The sum of three integers is 211."

a + b + c = 211

:

"The sum of the first an second integers exceeds the third by 39."

a + b = c + 39

a + b - c = 39

:

"The third integer is 23 less than the first."

c = a - 23:

Subtract the 2nd equation from the 1st equation

a + b + c = 211

a + b - c = 39

subtraction eliminates a and b, find c

2c = 172

c = 86:

Find a using the 3rd equation

86 = a - 23

86 + 23 = a

a = 109

:

Find b using the 1st equation

109 + b +86 = 211

b = 211 - 195

b = 16

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