Original Price Percent Increase

[mathdad]

Increasing the original price of an article by 15 percent and then increasing the new price by 15 percent is equivalent to increasing the original price by what percent?

The only thing I can do here is let x be the original price percent increase. Honestly, this percent question is ridiculously futile. When I see the word percent, I quickly think of 100 percent. What is the needed set up?

 

[MarkFL]

Let's let \(P_1\) be the original price. The final price, which we'll call \(P_2\) is obtained by increasing the original price by 15% twice:

$$P_2=1.15^2P_1$$

And so the percentage of increase \(I\) is:

$$I=100\frac{P_2-P_1}{P_1}\%=100(1.15^2-1)\%=\,?$$

 

[mathdad]

Let's let \(P_1\) be the original price. The final price, which we'll call \(P_2\) is obtained by increasing the original price by 15% twice:

$$P_2=1.15^2P_1$$

And so the percentage of increase \(I\) is:

$$I=100\frac{P_2-P_1}{P_1}\%=100(1.15^2-1)\%=\,?$$

Where did 1.15 come from? Tricky question, right?

 

[MarkFL]

Where did 1.15 come from?

Increasing something by 15% is the same as multiplying by 1.15:

$$x+x\cdot15\%=x+\frac{15}{100}x=x+0.15x=(1+0.15)x=1.15x$$

 

[mathdad]

Increasing something by 15% is the same as multiplying by 1.15:

$$x+x\cdot15\%=x+\frac{15}{100}x=x+0.15x=(1+0.15)x=1.15x$$

I assume x is what we are looking for.
I can convert 15 percent to 0.15 and 100 percent to 1.00 and add both to get 1.15.

Can you break down the process taken to arrive at your equation using the words in the application?

 

[MarkFL]

...Can you break down the process taken to arrive at your equation using the words in the application?

Which part wasn't clear?

 

[mathdad]

Just take me through the entire process from start to finish. I want to know what goes through your mind when creating an equation from a given application.

 

[Wilmer]

a = article

The "long" way:

1st increase: a + .15a = 1.15a

2nd increase: 1.15a + .15(1.15a) = 1.15a + .1725a = 1.3225a

So result = 32.25%

 

[mathdad]

I will be posting mostly word problems with work done to the best of my ability.

 

[Wilmer]

I will be posting mostly word problems with work done to the best of my ability.

Anybody that does "more" than his best is a liar :)

 

[MarkFL]

Just take me through the entire process from start to finish. I want to know what goes through your mind when creating an equation from a given application.

What I posted shows my thinking on solving the problem.

 

[mathdad]

Thank you everyone. I will mainly use the MHB for word problems. Practice makes perfect, right? So, I will search online and purchase word problem books to get enough practice.

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