Simplify and Solve

Date: 01/15/98 at 17:10:32
From: Claudia Cullen
Subject: Math question

Simplify one side of the equation. Then solve.

.75y + y + 10=45

We don't get it Please help?

Date: 01/19/98 at 10:24:53
From: Doctor Loni
Subject: Re: Math question

Don't feel bad! Learning to solve equations can be tough. Let's see if 
I can help a little bit.

In solving an equation like this, the goal is always to isolate (get 
by itself) the variable (in this case y ) on one side of the equation 
with a value on the other side. In other words, you want to find out 
what y equals.

The first step in solving is to get all the terms that have a y in 
them on one side of the equation. In your problem all the y's are 
already on one side. 

The next step is to combine all the terms with y in them (this could 
be called "simplifying one side"). In this case you have .75y + y
y by itself is actually 1y so you have

       .75y + 1y

It's just as if you had .75 apples + 1 apple = 1.75 apples 

     .75y + 1y = 1.75y

Now your equation looks like this:

      1.75y + 10 = 45

Since you have all your y's combined into one term, the next step is 
to get y by itself on one side of the equation. Since 10 is being 
added to your y term, subtract 10 from both sides of the equation 
(remember, whatever you do to one side of the equation you have to do 
to the other so they will still be equal to each other!)

       1.75y + 10 - 10 = 45 - 10

                 1.75y = 35

Right now you have 1.75y but you want to have just y (i.e. 1y) on the 
left side of your equation. To make 1.75 into 1, we need to divide 
(both sides, remember) by 1.75

          (1.75y)/1.75 = 35/1.75

        1.75/1.75 = 1 and 35/1.75 = 20      therefore

               1y = 20 or y = 20

If you want to check it, put 20 in for y in the original equation:

          .75(20) + 20 + 10 = 45

               15 + 20 + 10 = 45

                         45 = 45

Hope this helps - write back if you have another question.

-Doctor Loni,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/