# If the price of an apple was raised 50% and then decreased 50%, making it cost \$0.75, how much was the original price?

Asked by MissAnthrope (21462) November 29th, 2010

First of all, this is not a homework question. This is a ‘I’m not very good at math’ question. :)

I know it’s a simple enough question, but I answered it and now I’m not sure if my answer is right. The more I think about it, the more unsure I am.

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One dollar.

JLeslie (56899)

1.

ragingloli (44439)

Really?

YESSSSSSSS.

MissAnthrope (21462)

Is it a dollar?

I also suck at math.

KatawaGrey (21433)

@MissAnthrope So you got it right?

JLeslie (56899)

\$1.00

erichw1504 (26398)

Yep! I was torn, you know, because if you add 50% and take away 50%, you have a net change of 0%. But my gut told me that percentages are weird when adding and subtracting.

<happy dance>

It’s the small victories in life.

MissAnthrope (21462)

@MissAnthrope – you’re thinking adding and subtracting 50% of the original price. However, when you increase the price of something 50%, any subsequent decrease or increase is a percentage of the modified price.

So the percentages are of different amounts, and the net change isn’t zero. ;-)

iamthemob (17147)

Hahahaha. This is why when you hear the stock market went down 30% and the a month later you hear it is up 30% you need to know what number they are starting with. If someone started with \$100 stock, it goes down 30% you have \$70. Then it goes up 30% you have \$91, not the original \$100.

JLeslie (56899)

A bit late on the draw, but… \$1.00

YoBob (12823)

Thanks, guys! :D

MissAnthrope (21462)

Just in case you didn’t get it the first time, the answer is \$1.00

erichw1504 (26398)

So, it’s been confirmed many times over that you got the right answer. But did you go about it the right way? I’ll tell you how I thought about it, but I it’s probably not the only way to approach the problem.

First, I ignored the first part of the problem and simply focus on the fact that the price “decreased 50%, making it cost \$0.75.” Lets call the price x. Then we have:
x – 0.5x = 0.75 => x = 1.5

Now, I have the intermediate price, and I can consider the first part of the statement, “the price of an apple was raised 50%.” We know that the price was &1.50 after this change, because we just figured that out above. Let’s call the original price y. Then:
y + 0.5y = 1.5 => y = 1

Voila! We arrived at the correct answer.

To check:
The price of the apple was raised 50% => 1 + (0.5)(1) = 1.5
and then decreased 50% => 1.5 – (0.5)(1.5) = 0.75
making it cost \$0.75.

Perfect! Time for a happy dance. :)

bobbinhood (5894)

This question is from OkCupid, which I answered a month or so ago. I don’t remember how I worked this problem out, but I know I didn’t think of using Algebra. I’m pretty sure I did it the hard way. (story of my life!)

As soon as I saw your equation, I went, Duh, that would have been simple to solve with Algebra! Why didn’t I think of that? I wish I could give you more lurve. :)

Math genius I am not.

MissAnthrope (21462)

While my natural inclination is to use algebra, it is often not the most thoughtful way to approach a problem. I was once given a word problem in an education class full of math majors where we were forbidden to use algebra. It was interesting how much we struggled to find another (arguably simpler in that case) method. Either way, I’m glad I was able to help. :)

bobbinhood (5894)

It’s a very simple problem, actually.

Let x = the original value of the apple. Then the equation is:

1.5 x / 2 = \$0.75

Multiply both sides by 2:
1.5 x = \$1.50

Divide by 1.5:
x = \$1.00

CyanoticWasp (20063)

^^See? I never claimed to do things the simplest way.

@CyanoticWasp Would you mind explaining how you arrived at that equation?

bobbinhood (5894)

~12.48 Mexican Pesos, or 1 United States Dollar.

PhiNotPi (12670)

The original price was “x”. Increasing it by 50% means multiplying it by 1.5 (100% + 50% = 1.5). Decreasing that price by 50% means dividing by 2. So, 1.5 times x divided by 2. And we know what today’s price is: \$0.75, so that’s our equation:
1.5 x / 2 = \$0.75

CyanoticWasp (20063)

It’s original price was more than any regular apple should be, so this must have been some really GOOD apple. A Fugi maybe? So now we must bee talking yen. Oh my…..about 93 yen??

Don917 (180)

or