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Answer:
[tex]77, 385[/tex]
Step-by-step explanation:
Start by writing the equations in symbolic form. I will represent one number with an x and the other with a y.
One number is one-fifth of the other number:
[tex]x=\frac{1}{5}y[/tex]
The difference between the two numbers is 308:
[tex]y-x=308[/tex]
This difference is positive, therefore I am assuming that y is the larger number. In the first equation, I made x a part of y, so this should check out.
Now we have a system of equations:
[tex]\left \{ {{x=\frac{1}{5}y } \atop {y-x=308}} \right.[/tex]
I will rewrite the first equation for simplicity:
[tex]5x=y[/tex]
Now, I will substitute y from the first equation for y in the second equation:
[tex]5x-x=308[/tex]
Simplify:
[tex]4x=308\\x=77[/tex]
Now, use x to find y using the second equation:
[tex]y-77=308\\y=385[/tex]
Now, I can check the solutions by plugging them into the first equation!
[tex]x=\frac{1}{5}y\\ 77=\frac{1}{5}(385)\\77=77[/tex]
The solution is correct!