Rearranging Equation Help

[DaRafster]

P= S - C / S

Using the above equation, we are to rearrange it to make the subject "C"

Here is how I did it:

I first multiplied both sides by S

P x S = S - C

Then I subtracted S from both sides

P x S - S = - C

Then multiply both sides by (-1) to make C positive ----- I think this is where I went wrong

-P x (-S) + S = C

When I look at the solution it says the final equation is:

S - P x S = C

What did I do wrong?

 

[Romsek]

P= S - C / S

sorry to be pedantic but do you mean

[MATH]P = \dfrac{S-C}{S}[/MATH]
or

[MATH]P = S - \dfrac{C}{S}[/MATH]
it matters

 

[DaRafster]

sorry to be pedantic but do you mean

[MATH]P = \dfrac{S-C}{S}[/MATH]
or

[MATH]P = S - \dfrac{C}{S}[/MATH]
it matters

=S−CSP=S−CS\displaystyle P = \dfrac{S-C}{S}

The first one

Sorry if I wasn't clear!

 

[Dr.Peterson]

Then multiply both sides by (-1) to make C positive ----- I think this is where I went wrong

-P x (-S) + S = C

When I look at the solution it says the final equation is:

S - P x S = C

What did I do wrong?

You multiplied the left side by -1 twice!

When you multiply ab by -1, you don't get (-a)(-b); you just get -ab.

 

[Mr. Bland]

Welcome to Free Math Help!

If you don't have access to fraction notation, you need to use parentheses because division has a higher precedence than subtraction. It looks like this:

P = (S - C) / S​

Let's step through solving for [MATH]C[/MATH]:

[MATH]P = \frac{S - C}{S}[/MATH]​

I first multiplied both sides by S

P x S = S - C

Then I subtracted S from both sides

P x S - S = - C

So far so good!

[MATH]PS = S - C[/MATH]
[MATH]PS - S = -C[/MATH]​

Then multiply both sides by (-1) to make C positive ----- I think this is where I went wrong

-P x (-S) + S = C

What do you get when you multiply [MATH]-1 * PS[/MATH]? What you've written is equivalent to [MATH]-1 * P * -1 * S[/MATH].

 

[DaRafster]

Welcome to Free Math Help!

If you don't have access to fraction notation, you need to use parentheses because division has a higher precedence than subtraction. It looks like this:

P = (S - C) / S​

Let's step through solving for [MATH]C[/MATH]:

[MATH]P = \frac{S - C}{S}[/MATH]​

So far so good!

[MATH]PS = S - C[/MATH]​

​

[MATH]PS - S = -C[/MATH]​

What do you get when you multiply [MATH]-1 * PS[/MATH]? What you've written is equivalent to [MATH]-1 * P * -1 * S[/MATH].

Thank you - I got a final equation of -PS + S = C which I believe is is equivalent to C = S - P * S

 

[pka]

Given: \(\displaystyle p=\dfrac{S-C}{S}\)
Multiply by S, \(\displaystyle P\cdot S=S-C\)
Add \(\displaystyle C\) and subtract \(\displaystyle P\cdot S\) to get:
\(\displaystyle C=S-P\cdot S\)

 

[Steven G]

Here is why multiplying both number by -1 is wrong.

Consider this problem: 2*25*3*4. This is a very easy problem. The solution is just too quick to use a calculator. You CAN rearrange the numbers to get (2*3)*(4*25)= 6*100 = 600.

Now let's look at your problem. You had -p*(-s) = (-p)*(-s) = (-1*p)*(-1*s) = (-1*-1)*(p*s) = 1*(p*s) = p*s. Since you ended up multiplying by 1 (since (-1)*(-1)=1) and by -1 !!