Question 40731
30/10+Y= 20/10-Y

This problem is asking you to solve for y.  In order to solve for y, you must try to isolate the y to one side of the equation and all other terms to the other side of the equation.

This problem looks complicated, but it follows the same rules as:

a/b = c/x  Solve for x


The quickest way to solve for x is to cross-multiply:

a/b = c/x

ax = bc

Divide both sides by "a"

ax/a = bc/a

x = bc/a

So, going back to your original problem, treat each term in the fractions as a, b, c, or x.

30/10+Y= 20/10-Y

First, cross-multiply:

30(10-y = 20(10+y)

Simplify using the distributive property will give you:

300 - 30y = 200 + 20y

Solve for "y".  Remember, what you do to one side of the equation, you must do to the other side of the equation.

300 - 200 - 30y = 200 - 200 + 20y

100 - 30y = 20y

100 - 30 y + 30y = 20y + 30y

100 = 50y

100/50 = 50y/50

2 = y

Check to make sure this a true answer, by plugging "2" back into the orignial problem.

30/10+Y= 20/10-Y

30/10 + 2 = 20/10 - 2

30/12 = 20/8

2.5 = 2.5

The answer checks out!