SOLUTION: Hello, I have a question on solving formulas for variables. What are the steps for solving this problem. x/5 + 5y = m/n; solve for y Thank you

Question 467095: Hello,
I have a question on solving formulas for variables.
What are the steps for solving this problem.
x/5 + 5y = m/n; solve for y
Thank you
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your equation is:
x/5 + 5y = m/n
you want to solve for y.
subtract x/5 from both sides of the equation to get:
5y = m/n - x/5
divide both sides of the equation by 5 to get:
y = (m/n)/5 - (x/5)/5
(m/n)/5 is equivalent to m/(5n)
(x/5)/5 is equivalent to x/25)
your equation becomes:
y = m/(5n) - x/25
you can put everything under a common denominator to get:
y = 25m/(25*5*n) - 5nx/(25*5*h) which becomes:
y = (25m - 5nx) / (125n)
you can factor this further to get:
y = 5*(5m-nx) / (125n)
you can simplify this further to get:
y = (5m-nx) / (25n)
i think this is as far as you can go.
to confirm you did the process correctly, give some numbers to the variables and see if the equations are the same.
i let:
m = 2
n = 3
x = 4
using these values, the original equation of:
x/5 + 5y = m/n becomes:
4/5 + 5y = 2/3
subtract 4/5 from both sides to get:
5y = 2/3 - 4/5
divide both sides by 5 to get:
y = (2/3)/5 - (4/5)/5 which becomes:
y = 2/15 - 4/25
i'll stop there and see if i can duplicate that with the final equation.
the final equation is:
y = (5m-nx) / (25n)
after substitution this becomes:
y = (10 - 12) / 75
i have 2 equations.
the final equations shows up as y = (10 - 12) / 75
the original equation shows up as y = 2/15 - 4/25
i will get the original equation to have a common denominator.
the original equation becomes:
y = 10/75 - 12/75 which becomes (10 - 12) / 75
both equations are identical so the transformation was performed correctly.

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