SOLUTION: Not too long ago Edwin greatly helped me solve a system of equations from a word problem, it did indeed help me however, i need to now use that system and solve it using the substi

Question 73111: Not too long ago Edwin greatly helped me solve a system of equations from a word problem, it did indeed help me however, i need to now use that system and solve it using the substitution and elimination methods... can u help me?... the system is....
s + p + c = 40
c = 4p
s = p - 2

Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
s + p + c = 40
c = 4p
s = p - 2
---------------
The objective is to get an equation that has only one variable.
You are told c=4p
You are told s=p-2
Substitute that information into the 1st equation to get:
(p-2) +p +4p = 40
6p-2=40
6p=42
p=7
----------
Then c=4p=4*7=28
And s=p-2=7-2=5
---------
Solution:
p=7; s=5, c=28
==============
Cheers,
Stan H.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Notice how c=4p and s=p-2, you can simply replace c and s in the first equation with 4p and p-2. This allows you to work with nothing but p.

Replace c with 4p (it's like saying x+5=10 and if I replace x with 5 I get 5+5=10. What I'm doing is substituting 5 into x to show that they are equal. In this case I'm working with p's and c's).
Do the same thing to s and replace s with p-2
Now we have gone from 3 variables to 1 variable. We can now solve for p.
Group like terms
Add like terms and add 2 to both sides
Divide both sides by 6

Now that we have p=7 we can use this to solve for c and s
Solving for c

Solving for s

So p=7, s=5, and c=28

Check:
Use the first equation

Works

Use the 2nd equation

Works

Check with the 3rd equation

Works
Hope this helps.

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