# Harry's Discount

• Sep 26th 2010, 09:59 AM
Hellbent
Harry's Discount
Hi,

I need the reasoning behind the answer for this question explained, please.

At Harry’s Discount Hardware everything is sold for 20% less than the price marked. If Harry buys tool kits for \$80, what price should he mark them if he wants to make a 20% profit on his cost?

My reasoning was to find 20% of 80 then subtract it from 80, then add it back and the answer would be 80. Upon recognizing the abject failure of this attempt I reasoned it another way: he wants to make a 20% profit and the discount for everything would be 20%, so I found 40% of 80, 32, and added it to 80. The answer equaling \$112. I used 40% because splitting it in half gives 20 a piece. One of the 20%'s is the profit and the other is the discount.

In truth my understanding of the question is a little murky and my reasoning skills are unenviable.
• Sep 26th 2010, 10:33 AM
Pim
Okay, the problem with percentages is, that you can't just "split them in half". Percentages are relative to something. In this case, the 20% discount is relative to the pricetag, while the 20% profit is relative to the \$80 Harry buys toolkits for.

So, he wants to make 20% profit.
This means he wants to receive 0.20*80+80=\$96
This does not yet include the discount.
Then he wants to price it as such, that once the discount is calculated, what is left over is \$96.
This means \$96 is equal to 80% (100%-20%)

Therefore you need to solve 0.80*x=\$96, and x is the price that goes on the price tag.

Does this make it clear?
• Sep 26th 2010, 07:23 PM
Hellbent
I get the first part. Though I wonder if the discount could have been found first.

Quote:

Originally Posted by Pim
This means \$96 is equal to 80% (100%-20%)

Therefore you need to solve 0.80*x=\$96, and x is the price that goes on the price tag.

Does this make it clear?

I'm not understanding this part. Why did you subtract 20% from 100%? I'm not entirely sure how you arrived at the equation. Division seems a good choice but I don't understand why. I multiplied 96 by 0.80, result never made sense. Added 20% of 80 to 96, 112, made sense (only because 112 is an answer option). Essentially I'm just guessing.
• Sep 26th 2010, 10:21 PM
Pim
So, my reasoning was the following:

You have the pricetag that Harry puts on the tool kit. Let's call this price "x". Now, a customer walks in, and he sees the sign "Everything 20% off". Therefore if he sees a pricetag of \$100, he expects to pay \$80. (This is how percentages are relative.)
Now, the customer sees the price tag of "x". x must be chosen as such that he expects to pay \$96. (This way Harry makes his 20% profit.)
Therefore, the price x, can be split in two parts: 80% is the price he actually pays (\$96), 20% is the discount.

Normally, if you calculate a percentage of something, you can multiply by the percentage divided by hundred. Therefore, the price (x) multiplied by 80/100 (0.8) should be equal to \$96

I don't know how much experience you have with solving equations. So, I'm going to teach you a relatively simple, but un-mathematical trick.

So, you know 0.80*x=\$96
You can compare this to 2*3=6
You know that 3 = 6/2
Therefore, x = \$96/0.80 = \$120