Problem Set Four

Second problem solving assignment. Yay math!

1) Question:
The price of each item at the Gauss Gadget store has been reduced by 20% from it's original price. An MP3 player has a sale price of $112.00. What would the same MP3 player sell for if it was on sale for 30% off it's original price?

2) Answer:
I'll just break into equations.

To begin, we should find the original price.
To find the original price, I'll divide $112.00 by 80, since that's the percent of the full price that is left (100% - 20% = 80% price, which means, x - y = $112.00).
$112.00/80 = $1.40. That means that 1% of the product is the equivalent of $1.40.
To find out the original price, we have to find out how much the 20% that was removed is worth in dollars. 20%*$1.40 = $28.00.
Now we can get the original price. As I have previously stated, 100% - 20% = 80%, so 80% + 20% = 100%. In other words, $112.00 + $28.00 = x.
The original, full price, x, is $140.00. (You can also find this by taking $1.40 and multiplying it by 100%).

Now we're looking for a 30% sale price. The original price remains constant.
So, the equation we're working with is: Original Price - 30% off = Sale Price, or $140.00 - z = a, a being the 30%-off sale price.
We can find the 30% off by using the same method as we did for finding 20%. Take $1.40 and multiply it by 30 to get the 30%. The answer is $1.40*30% = $42.00.
The amount saved with the 30% off sale is $42.00. Referring back to the equation we had earlier, that means $140.00 - $42.00 = a. $140.00 - $42.00 = $98.00.

With a 30% off sale, the MP3 player would cost $98.00.

In summary, and if you'd rather just get it all out of the way and see a dumbed-down version of the same question:
i) Take $112.00 and divide it by 80. This is because $112.00 is 80% of the original cost. You will get an answer of $1.40.
ii) Multiply $1.40 by 100 to get the full price. You will get an answer of $140.00.
iii) Multiply $1.40 by 30 to get the amount off for the 30%-off sale price. You will get an answer of $42.00.
iv) Take the full price ($140.00) and subtract the 30% sale ($42.00). You will get an answer of $98.00.

3) I wasn't originally going to do this question, but Margo brought it up so I used it. I dislike working with finding percentages of numbers, but this one turned out to be easier than I remember with percentages. So, I guess I can say I like it because I felt I am understanding percentages more.

4) I learned more about using percentages through this question, and finding amounts based on percentages that are based on amounts (make sense of that!). That's really the main thing, since I'm normally not so good with working with percentages.

The end.