Question 1097069
<br>Let the numbers be, in order, A, B, and C.<br>
The first of 3 numbers exceeds the third by 1/2 of the second:
{{{A = C + (1/2)B}}}  (1)<br>
The sum of second and third is one more than the first:
{{{B+C = A+1}}}  (2)<br>
If the second is subtracted from the sum of the first and third numbers the result is 5:
{{{A+C-B = 5}}}  (3)<br>
The three equations we get by translating the given information directly are all in different forms; so it is not clear what might be the best way to solve the system.  So I hope you get other answers from other tutors.... But this is the way I went:<br>
Substituting (1) into (2) gives us<br>
{{{B+C = C + (1/2)B + 1}}}
{{{B = (1/2)B+1}}}
{{{(1/2)B = 1}}}
{{{B = 2}}}<br>
Substituting the value of B into (2) and (3) gives us<br>
{{{C+2 = A+1}}} and {{{C-2 = -A+5}}}<br>
Adding those two equations gives us<br>
{{{2C = 6}}}
{{{C = 3}}}<br>
Then substituting the values of B and C into any of the original equations gives us A=4.<br>
So the numbers are, in order, 4, 2, and 3.