Question 1052912
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 + {{{1/2}}}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 + {{{1/2}}}b
b - {{{1/2}}}b = 3 - 2
{{{1/2}}}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