SOLUTION: The first of three numbers exceeds the third by one-half of the second. The sum of the second and the third numbers is one more than the first. If the second is subtracted from the

Question 1052912: The first of three numbers exceeds the third by one-half of the second. The sum of the second and the third numbers is one more than the first. If the second is subtracted from the sum of the first and third numbers the result is 5. Determine the numbers.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Three numbers; a, b, c
:
Write an equation for each statement
The first of three numbers exceeds the third by one-half of the second
a = c + b
The sum of the second and the third numbers is one more than the first.
b + c = a + 1
If the second is subtracted from the sum of the first and third numbers the result is 5.
a + c - b = 5
:
Rearrange the 2nd and 3rd equations for elimination
-a + b + c = 1
a - b + c = 5
-----------------Addition eliminates a and b, find c
0 + 0 + 2c = 6
c = 6/2
c= 3
:
using the 2nd equation replace c with 3
b + 3 = a + 1
a = b + 2
In the first equation replace c with 3, and a with (b+2)
b + 2 = 3 + b
b - b = 3 - 2
b = 1
multiply equation by 2
b = 2
then
a = 2 + 2
a = 4
:
Determine the numbers. 4, 2, 3
:
:
Check solution in the last statement
"If the second is subtracted from the sum of the first and third numbers the result is 5."
4 + 3 - 2 = 5
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