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

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> 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       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
18.95w+%2B+19.50r+=+572.90 Start with the given equation.


1895w+%2B+1950r+=+57290 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:

system%28w%2Br=30%2C1895w%2B1950r=57290%29


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

w%2Br=30 Start with the first equation


r=30-w Subtract w from both sides


r=-w%2B30 Rearrange the equation


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

Since r=-w%2B30, we can now replace each r in the second equation with -w%2B30 to solve for w



1895w%2B1950highlight%28%28-w%2B30%29%29=57290 Plug in r=-w%2B30 into the second equation. In other words, replace each r with -w%2B30. Notice we've eliminated the r variables. So we now have a simple equation with one unknown.



1895w%2B%281950%29%28-1%29w%2B%281950%29%2830%29=57290 Distribute 1950 to -w%2B30


1895w-1950w%2B58500=57290 Multiply


-55w%2B58500=57290 Combine like terms on the left side


-55w=57290-58500Subtract 58500 from both sides


-55w=-1210 Combine like terms on the right side


w=%28-1210%29%2F%28-55%29 Divide both sides by -55 to isolate w



w=22 Divide





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


So the first part of our answer is: w=22









Since we know that w=22 we can plug it into the equation r=-w%2B30 (remember we previously solved for r in the first equation).



r=-w%2B30 Start with the equation where r was previously isolated.


r=-%2822%29%2B30 Plug in w=22


r=-22%2B30 Multiply


r=8 Combine like terms



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


So the second part of our answer is: r=8









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

So our answers are:

w=22 and r=8