The original cost of a coat was increased by 40% at the beginning of 2015. In March 2015, the new price was reduced by 20%, and the cost remained at this new reduced price. Chris had a coupon for a $ 50 discount and, in April, used the coupon to buy the coat at the further reduced price. There was no tax or additional fee on the purchase. If Chris paid $ 95.60 for the coat, which would be the original price of the coat?

A. $ 92.50

B. $ 100

C. $ 104.83

D. $ 120

E. $ 130
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Same answer I got. Cannot see how answer could be C.

I do not understand this procedure.

We know a certain price is reduced by 20% to a final price of 145.6. Knowing this, we do

X - 0.2X = 145.6

X(1 - 0.2) = 145.6

X(0.8) = 145.6

X = 145.6/0.8 = 182

Further, we know this new price was obtained by increasing the original price by 40%, so

X + 0.4X = 182

X(1 + 0.4) = 182

X(1.4) = 182

X = 182/1.4 = 130


In particular, this line is why I think the solution doesn't make sense to me:



Discounting something by 20% does not work back in reverse directly. Example: I discount a price of 100 by 20% to obtain a new price of 80. However, this does not work in reverse like in your example: 80 x 1.2 = 96, not 100. Therefore, 145.6 * 1.2 = $ 174.72 is lower than the actual value you need.(<182)

This is the same principle behind why people say that a company which has a drop in share value will need to gain back more value to get back to the same spot as before. Losing 20% of the share price means you will have to get back 25% to get back to the same spot: 100 - 20% = 80. 80 x 1.25 = 100.

I cannot really explain my side of the calculations more than I already have so I will address



I am also working backward. I would like to clarify that the 20% we are adding back is not 20% of 145.6, but 20% of the original unknown price. To rephrase it:

Unknown price X is > 145.6

Decrease X by 20% first: we take 0.2*X, which is equal to 20% of unknown price X, and then subtract it from X to arrive at a new decreased price of 145.6

Here is a comparison to my simpler example for each step

X - 0.2(X) = 80
X - 0.2(X) = 145.6

X(0.8) = 80
X(0.8) = 145.6

X = 80/0.8 = 100
X = 145.6/0.8 = 182


Notice the error is in the 20% you take.

We all agree 80*1.2 =/= 100.
We all agree 80*1.25 = 100.

This means we KNOW we should not multiply by 1.2, but instead by 1.25.



If we are asked to find the original price, which at some point was modified by 20% off, then I will have to incorporate that 20% off to work backwards and find it. I don't know if we just don't agree on the phrasing used in the question but I will ask some people to double check this for me.

EDIT; I appreciate you taking the time to write out your explanations. I've asked some other people to double check this for what I'm having an issue understanding about the original prompt.

Any explanation of calculations in book?

It was just an example to illustrate percentage gains and losses and why it's harder get back to your previous value after negative shift.

Example:

I have 1 share of company that is worth $100.

If value of the share drops by 20%, my new value of the share is $80.

If I want to get back to the original value of the share ($100), the share price would have to increase by 25%.

80*1.25 = 100.

In the end, a loss of 20% has lost us $20, but to make up those SAME $20, we would have to gain 25%.

Difference in 5% to make up the same dollar value. Hence, easy to lose, hard to gain.