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You have 2 positive numbers. One number is one-fifth of the other number. The difference between the two numbers is 308, find the numbers. PLEASE HELP

User Bitgarden
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1 Answer

2 votes

Answer:


77, 385

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:


x=(1)/(5)y

The difference between the two numbers is 308:


y-x=308

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:


\left \{ {{x=(1)/(5)y } \atop {y-x=308}} \right.

I will rewrite the first equation for simplicity:


5x=y

Now, I will substitute y from the first equation for y in the second equation:


5x-x=308

Simplify:


4x=308\\x=77

Now, use x to find y using the second equation:


y-77=308\\y=385

Now, I can check the solutions by plugging them into the first equation!


x=(1)/(5)y\\ 77=(1)/(5)(385)\\77=77

The solution is correct!

User SpacemanScott
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