I have a question on how to solve an equation...

[Goncarfabian]

The equation is
(P×11.5%)+P=T
How do I isolate the variable P?

 

[Dr.Peterson]

The equation is
(P×11.5%)+P=T
How do I isolate the variable P?

You might start by factoring out P on the left-hand side.

 

[skeeter]

change 11.5% to a decimal, then factor

 

[HallsofIvy]

11.5% is 0.115 so "Px11.5%+ P" is "0.115P+ P= (0.115+ 1)P= 1.115P

 

[MrFahrenheit]

Taking the n% is the same as multiplying by n/100, use this to turn the equation into a linear equation

 

[pka]

Taking the n% is the same as multiplying by n/100, use this to turn the equation into a linear equation

Really \(n\%=n\cdot 10^{-2}\) In this case because \(11.5=115\cdot 10^{-1}\) we get \(11.5\%=115\cdot 10^{-3}=0.115\)

 

[Otis]

Really \(n\%=n\cdot 10^{-2}\) …

Yes, that's really true also.

\(\;\)

 

[Otis]

Taking the n% is the same as multiplying by n/100, use this to turn the equation into a linear equation

Good hint. 11.5% of P is the same as P×11.5/100

Here's another tip for students: Recall that dividing or multiplying decimal numbers by powers of 10 is as easy as shifting the decimal point. For example, dividing by 100 is the same as shifting the decimal point two places to the left.

So 11.5/100 becomes 0.115 and we write 0.115P instead of P×11.5%

PS: Once we get into algebra, we mostly stop writing × to mean multiplication because it looks too much like the variable x. In the forum, we could use an asterisk to show multiplication. (In simple expressions, we don't a multiplication symbol.)

0.115*P + P = T

0.115P + P = T

Cheers ?

 

[Otis]

How do I isolate the variable P?

Hi Goncarfabian. We've simplified the equation for you, using the decimal form of 11.5%

0.115P + P = T

Dr. Peterson suggested factoring the left-hand side. Halls did that for you.

P(0.115 + 1) = T

Halls did the addition for you, too.

P(1.115) = T

Can you do the last step?

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