Respuesta :
Answer:
The three numbers from the largest to the smallest are:
43, 20 and -7
Explanation:
Let the three numbers be: x, y and z.
Since their sum is 56, we have:
[tex]x+y+z=56[/tex]Suppose z is the largest, and x, the smallest. As their difference is 50, we have:
[tex]z-x=50[/tex]Lastly, given that the sum of the two smaller numbers is 13, we have:
[tex]x+y=13[/tex]We want to find the values of x, y and z.
Using the last equation in the first equation, we can replace (x+y) by 13 to have:
[tex]13+z=56[/tex]Subtracting 13 from both sides, we have:
[tex]\begin{gathered} z=56-13 \\ z=43 \end{gathered}[/tex]Now, using z = 43 in the second equation, we have:
[tex]43-x=50[/tex]Subtracting 43 from both sides
[tex]\begin{gathered} -x=50-43 \\ -x=7 \end{gathered}[/tex]Divide both sides by -1
[tex]\begin{gathered} x=\frac{7}{-1} \\ \\ x=-7 \end{gathered}[/tex]Finally, using x = -7 in the third equation, we have:
[tex]-7+y=13[/tex]Add 7 to both sides
[tex]\begin{gathered} y=13+7 \\ y=20 \end{gathered}[/tex]Therefore, the three numbers from the largest to the smallest are:
43, 20 and -7
