Given that the sum of three numbers is forty-nine. The sum of the first and third number is nine less than the second, and the third number is a quarter of the second.
Derive a system of equations representing the information given.
Let's call those three numbers `x,y` and `z.` Their sum is 49 hence
Sum of the first and third is nine less than the second hence
The third is quarter of the second hence
So you have system of three equations with three variables.
Now you can solve this system by using Gauss elimination or some other method.
Your final solution is `x=51/4,` `y=29` and `z=29/4.`
`z=1/4 y` (3)
Subtracting (5) from (4):
`2y=58` `rArr y=29`
so from (1):
`x+ 145/4 =49`
so the solutions are:`x=51/4;y=29;z=29/4`