# Original Price Percent Increase

• MHB
In summary: 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=1.15xIn summary, increasing the original price by 15 percent and then increasing the new price by 15 percent is equivalent to increasing the original price by what percent?
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?

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:

$$\displaystyle P_2=1.15^2P_1$$

And so the percentage of increase $$I$$ is:

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

MarkFL said:
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:

$$\displaystyle P_2=1.15^2P_1$$

And so the percentage of increase $$I$$ is:

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

Where did 1.15 come from? Tricky question, right?

RTCNTC said:
Where did 1.15 come from?

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

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

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

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

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?

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

Which part wasn't clear?

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.

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%

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

RTCNTC said:
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 :)

RTCNTC said:
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.

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.

Word Problems Will Cover:

GED
ASVAB
GMAT
SAT 1 & 2
GRE
CUNY ENTRANCE TEST
ONLINE SITES

## 1. What is the formula for calculating original price percent increase?

The formula for calculating original price percent increase is: (Final Price - Original Price) / Original Price x 100.

## 2. Can original price percent increase be negative?

No, original price percent increase cannot be negative. It represents the percentage increase from the original price to the final price.

## 3. How do I calculate the new price after a percentage increase?

To calculate the new price after a percentage increase, multiply the original price by 1 plus the percentage increase (in decimal form). For example, if the original price is $100 and the percentage increase is 20%, the new price would be$100 x (1 + 0.20) = \$120.

## 4. Can original price percent increase be greater than 100%?

Yes, original price percent increase can be greater than 100%. This means that the final price is more than double the original price.

## 5. How is original price percent increase useful in business?

Original price percent increase is useful in business for calculating changes in prices, determining profit margins, and evaluating the success of sales and marketing strategies.

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