SOLUTION: The sum of three integers is 69. The sum of the first an second integers exceeds the third by 93. The third integer is 10 less than the first. Find the three integers.
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-> SOLUTION: The sum of three integers is 69. The sum of the first an second integers exceeds the third by 93. The third integer is 10 less than the first. Find the three integers.
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Question 579851: The sum of three integers is 69. The sum of the first an second integers exceeds the third by 93. The third integer is 10 less than the first. Find the three integers. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! The sum of three integers is 69. The sum of the first an second integers exceeds the third by 93. The third integer is 10 less than the first. Find the three integers.
:
Write an equation for each statement:
:
"The sum of three integers is 69."
a + b + c = 69
:
"The sum of the first an second integers exceeds the third by 93."
a + b = c + 93
a + b - c = 93
:
"The third integer is 10 less than the first."
c = a - 10
:
Subtract the 2nd equation from the 1st equation
a + b + c = 69
a + b - c = 93
---------------subtraction eliminates a and b, find c
2c = -24
c = -12
:
Find a using the 3rd equation
-12 = a - 10
-12 + 10 = a
a = -2
:
Find b using the 1st equation
-2 + b - 12 = 69
b = 69 + 14
b = 83
:
The three integers:
a = -2
b = +83
c = -12
---------
sum +69
:
Check in the 2nd equation
a + b = c + 93
-2 + 83 = -12 + 93
81 = 81
