SOLUTION: Two numbers are added and the sum is s, and their difference is 1/mth of the larger. Determine the numbers. Let x and y = the numbers. Let y = larger. An equation provid

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Question 1043108: Two numbers are added and the sum is s, and their difference is 1/mth of the larger. Determine the numbers.
Let x and y = the numbers. Let y = larger.
An equation provided with problem:
x - (s - x) = x/m.

My partial attempt:
x + y = s
y - x = 1/m * y.

How do I proceed ?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!


system%28x%2By=s%2Cy-x=expr%281%2Fm%29%2Ay%29

Solve the first equation of the system for y

x%2By%22%22=%22%22s%29

y%22%22=%22%22s-x%29

Now substitute (s-x) for y in the second equation of the system.

y-x=expr(1/m)*y

%28s-x%29-x=expr%281%2Fm%29%2A%28s-x%29

Multiply through by m

m%28s-x%29-mx=s-x

ms-mx-mx=s-x

ms-2mx=s-x

x-2mx=s-ms

x%281-2m%29=s-ms%29

x=%28s-ms%29%2F%281-2m%29

y%22%22=%22%22s-x%29

y%22%22=%22%22s-%28s-ms%29%29%2F%281-2m%29%29

y%22%22=%22%22%28s%281-2m%29%29%2F%281-2m%29-%28s-ms%29%2F%281-2m%29

y%22%22=%22%22%28s-2ms%29%2F%281-2m%29-%28s-ms%29%2F%281-2m%29

y%22%22=%22%22%28%28s-2ms%29-%28s-ms%29%29%2F%281-2m%29

y%22%22=%22%22%28s-2ms-s%2Bms%29%2F%281-2m%29

y%22%22=%22%22%28-ms%29%2F%281-2m%29

Multiply top and bottom by -1

y%22%22=%22%22%28ms%29%2F%28-1%2B2m%29

y%22%22=%22%22%28ms%29%2F%282m-1%29


Edwin