Answer:
[tex]\begin{gathered} \text{First number=16} \\ \text{second number=22} \\ \text{Third number=66} \end{gathered}[/tex]
Explanation:
Let the unknown numbers be x, y, and z where
• First number = x
,
• Second number = y
,
• Third number = z
If the sum of the three numbers is 104, then;
[tex]x+y+z=104[/tex]
If the first number is 6 less than the second, hence;
[tex]\begin{gathered} x=y-6 \\ \end{gathered}[/tex]
Also, if the third number is 3 times the second, then;
[tex]z=3y[/tex]
Substitute equations 2 and 3 into equation 1 to reduce the variables to the function of "y" only:
[tex]\begin{gathered} x+y+z=104 \\ (y-6)+y+3y=104 \\ y-6+4y=104 \\ 5y-6=104 \\ 5y=104+6 \\ 5y=110\rbrack \\ y=\frac{110}{5} \\ y=22 \end{gathered}[/tex]
Get the first number "x"
[tex]\begin{gathered} x=y-6 \\ x=22-6 \\ x=16 \end{gathered}[/tex]
Get the third number "z"
[tex]\begin{gathered} z=3y \\ z=3(22) \\ z=66 \end{gathered}[/tex]
Therefore the three numbers are 16, 22, and 66.
