Expert: Josh - 3/15/2007

Question

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Yes, you have provided the correct solution.  If I understand correctly. Is the following correct. I'll use $100 as the initial cost:

1. Discounted Price = (1 - 4%) X Initial Cost of $100 =
(1 - 4%) X 100 = 60% X $100 = $60 = Discounted Price

2.  Initial Cost X = Y/0.6. This will be $100 = $60/60%

3. Actual Saving is 0.4*X, which is equivalent to Y*R/(1 - R), where R = 40/100.
This is ($0.6 X 40/100)/(1 - 40/100) = (0.6 X 40/100)/(1 - 40/100) = 0.24/0.6 = 0.4 or 4%

4. I saw this on a grocery bag "Save 40%". I assume that for every $1.00 that someone spends in a grocery store, he will spend $0.60 in the store advertising the 40% savings.

I thank you for your help and assistance.

The text above is a follow-up to ...
-----Question-----
Hello:

How can someone determine how he saved 40% on his grocery expenses?

I thank you for your reply.
-----Answer-----
I don't understand your question. Do you mean this -- given the discounted total, determine the actual saving offered by the 40% discount?

If so, we let X by the total cost without discount.
With the 40% discount, the discounted total is Y = (1 - 0.4)* X. i.e., initial cost X = Y/0.6. So, the actual saving is 0.4*X, which is equivalent to Y*R/(1 - R), where R = 40/100.

Answer
There are couple of things I should mention.

In part 1:
 0.40 (40/100) is 40%, not 4%.

In part 3:
 Y=60 dollars, not 0.6.
 Actual saving is Y*R/(1-R)=60*0.4/0.6=40 dollars

Re: Part 4
 Advertising is always misleading. First question we should ask is what the 40% is relative to? Second question is whether the price tag has already been marked-down. Or is there still a further 40% discount on marked prices. Make sure you ask. A mathematically correct assumption is not always the same assumption as that of the shop-owner.