Percent & Discounts: confused by the "... rug of equal value...".

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KWF

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Dealer A offers a rug for $450, less 33 &1/3% and 20%. Dealer B offers a rug of equal value for $500, less 30%, 20%, and 10%.
Which is the better offer and how much better?

Is this solution correct?

Dealer A: $450 – (8/15 * $450) = $450 - $240 = $210

(I converted 33&1/3%5 to 1/3 and 20% to 1/5 and added these two fractions to get 8/15)

Dealer B: $500 – (60% * $500) = $500 - $300 = $200

Dealer B has the better offer by $210 - $200 = $10.00

I am somewhat confused by the "... rug of equal value...". I think it indicates of equal quality not the same price of $450. (?)
 
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KWF said:
Dealer A offers a rug for $450, less 33 &1/3% and 20%. Dealer B offers a rug of equal value for $500, less 30%, 20%, and 10%.
Which is the better offer and how much better?

Is this solution correct?

Dealer A: $450 – (8/15 * $450) = $450 - $240 = $210

(I converted 33&1/3%5 to 1/3 and 20% to 1/5 and added these two fractions to get 8/15)

Dealer B: $500 – (60% * $500) = $500 - $300 = $200

Dealer B has the better offer by $210 - $200 = $10.00

I am somewhat confused by the "... rug of equal value...". I think it indicates of equal quality not the same price of $450. (?)
Click to expand...
Yes, it is an atrociously worded problem.

I too think it means that the two rugs are of equal quality.

If the intent of the problem is to say that Dealer 1 discounts the rug originally listed at 450 by 8/15 of the listed price, why not just say so? You are not studying how to add fractions.

So I am guessing that what is meant is that Dealer 1 discounts the rug originally listed at 450 first to 300 (two thirds of 450) and then to 240 (four fifths of 300).

If that is what is meant, then Dealer 2 discounts the rug originally listed at 500 first to 350, second to 280, and third to 252.

The mathematical conclusion is that Dealer 1 is less of a thief than Dealer 2.
 
450*(1 - 1/3)*(1 - .2) = 240

500*(1 - .3)*(1 - .2)*(1 - .1) = 252
 
KWF said:
Dealer A offers a rug for $450, less 33 &1/3% and 20%. Dealer B offers a rug of equal value for $500, less 30%, 20%, and 10%.
Which is the better offer and how much better?

Is this solution correct?

Dealer A: $450 – (8/15 * $450) = $450 - $240 = $210

(I converted 33&1/3%5 to 1/3 and 20% to 1/5 and added these two fractions to get 8/15)

Dealer B: $500 – (60% * $500) = $500 - $300 = $200

Dealer B has the better offer by $210 - $200 = $10.00

I am somewhat confused by the "... rug of equal value...". I think it indicates of equal quality not the same price of $450. (?)
Click to expand...
In order to find out which *deal* is better we have to start off with the same exact rug.

Dealer A first offers a 33 1/3% discount and then offers an additional 20% off. You do not add the two discounts. Same with Dealer B. Others showed how to do the work.
 
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Jomo said:
In order to find out which *deal* is better we have to start off with the same exact rug.

Dealer A first offers a 33 1/3% discount and then offers an additional 20% off. You do not add the two discounts. Same with Dealer B. Others showed how to do the work.
Click to expand...

Why is it incorrect to "... not add the two discounts. Same with Dealer B."?
 
KWF said:
Why is it incorrect to "... not add the two discounts. Same with Dealer B."?
Click to expand...

If I offer you a $100 item with a 50% discount, then another 50% discount, what is the final price?
 
lev888 said:
If I offer you a $100 item with a 50% discount, then another 50% discount, what is the final price?
Click to expand...


I hope that this is not a rhetorical question. If not, the solution is as follows:

$100.00 - 100% is $0.00. (If the two percentages are added)

$100 - 50% is $50 - another 50% is $50 - $25 is $25.

Thanks for the clarification!
 
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