SOLUTION: Is there anyone out there that could help me solve a problem? I'm not sure what they even want. Thank-you very much. w+r=30 18.95w + 19.50r = 572.90 Find the values

Question 191949: Is there anyone out there that could help me solve a problem? I'm not sure what they even want. Thank-you very much.

w+r=30
18.95w + 19.50r = 572.90
Find the values for w and r.
Bittenger, M.L. & Beecher, J.A. (2007). Introductory and intermediate algebra (3rd ed.).
Boston: Pearson-Addison Wesley

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Multiply EVERY term by 100 to move the decimal point 2 spots to the right (which makes every number a whole number)

So we have the system of equations:

Let's solve this system by substitution

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for r.

So let's isolate r in the first equation

Start with the first equation

Subtract from both sides

Rearrange the equation

---------------------

Since , we can now replace each in the second equation with to solve for

Plug in into the second equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute to

Multiply

Combine like terms on the left side

Subtract 58500 from both sides

Combine like terms on the right side

Divide both sides by -55 to isolate w

Divide

-----------------First Answer------------------------------

So the first part of our answer is:

Since we know that we can plug it into the equation (remember we previously solved for in the first equation).

Start with the equation where was previously isolated.

Plug in

Multiply

Combine like terms

-----------------Second Answer------------------------------

So the second part of our answer is:

-----------------Summary------------------------------

So our answers are:

and

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