Math help

I freely admit that I'm not a math genius but I can't seem to get to the right answer on this math problem (of my 13 year old). Will you all help me?

Here is the problem, verbatim:

At her store, Stella sells clothing for 60% more than she paid. During a weekend sale, she sold clothing for 12.5% off what she would normally charge. Her revenues, including the 6% Florida Sales tax, totaled $29,680. How much did Stella pay, in dollars, for clothing sold that weekend?

Answer?

Let's get rid of the tax first: multiply 29680 by (100/106) to get the amount the clothes retailed for: $28000.

She sells them for 60% more than she paid, so 28000 is 160% of what she paid. (100/160) * 28000 = 17500

$17,500.

It's more intuitive running it forward to check:

Markup: $17,500 * 160% = $28,000.
Tax: $28,000 * 106% = $29,680.

In reply to ransom:

You forgot the clothes were 12.5% off that weekend.

So I'm confused even more. To start with, I thought this was the equation to get rid of the tax (hey...at least I thought to do that!).

$29680 x .06 = $1780.80
$29680 - $1780.80 = $27899.20

19130.88 ?

minus the sales tax I have 27899.20 as total store revenue, revenue times .94.

she had a sale for 12.5% off... so divide by .875, or multiply by 1.125, to get actual revenue before the sale, 31884.80.

Cost is 31884.80 times .6 to equal cost, 19130.88.

I could be wrong, but that is my answer.

All i know is i am in the wrong business should be selling clothes

Ranger50 wrote: 19130.88 ? minus the sales tax I have 27899.20 as total store revenue, revenue times .94. she had a sale for 12.5% off... so divide by .875, or multiply by 1.125, to get actual revenue before the sale, 31884.80. Cost is 31884.80 times .6 to equal cost, 19130.88. I could be wrong, but that is my answer.

Isn't 27899.20 x 1.125 equal to 31386.60?

Im going with 296809(.94)(.875)(1/1.6)=15257.38

Kenny_McCormic wrote: In reply to ransom: You forgot the clothes were 12.5% off that weekend.

Gah, reading comprehension fail! So embarrassed...

Get rid of the sales tax: (29680/106)*100=28000

Undo the 12.5% discount: 28000*1.125=31500

Lop off Stella's enormous profit margin: (31500/160)*100=19687.50

I really hope that's right, I keep checking it over and I'll feel like a huge moron if it's not.

dyintorace wrote:

Ranger50 wrote: 19130.88 ? minus the sales tax I have 27899.20 as total store revenue, revenue times .94. she had a sale for 12.5% off... so divide by .875, or multiply by 1.125, to get actual revenue before the sale, 31884.80. Cost is 31884.80 times .6 to equal cost, 19130.88. I could be wrong, but that is my answer.

Isn't 27899.20 x 1.125 equal to 31386.60?

I divided by .875. the maths are different. never figured it out way either. dealership I worked at did the same thing.

dyintorace wrote: So I'm confused even more. To start with, I thought this was the equation to get rid of the tax (hey...at least I thought to do that!). $29680 x .06 = $1780.80 $29680 - $1780.80 = $27899.20

To address these things one at a time, the problem with what you've done above is that the tax is 6% of the retail price, but you've subtracted 6% of the combination of retail price and tax. That is, you're subtracting 6% of 106% of the original value...

In numbers:
100% * 106% = 106% of the original value
106% * 6% = 6.36% (what you're going to subtract is larger than what you added)
106% - 6.36% = 99.64%

GameboyRMH wrote: Get rid of the sales tax: (29680/106)*100=28000 Undo the 12.5% discount: 28000*1.125=31500 Lop off Stella's enormous profit margin: (31500/160)*100=19687.50 I really hope that's right, I keep checking it over and I'll feel like a huge moron if it's not.

Lol, this is one of the funniest threads I have seen in a while ... we are all trying to do 13 year old math and cant come up with the same answer. Thanks god I am not homeschooling ... but this is what I got:

29680 x (100/106) = 28000 tax gone

28000 x (100/87.5) = 32000 discount gone

32000 x (100/160) = 20000 ... cost.

So diy ... tells us that at least this is multiple choice and you have the answer ... (I am afraid to say that I am an ME ... it might come back and bite me in the ass, lol)

J

Slippery wrote: 29680 x (100/106) = 28000 tax gone 28000 x (100/87.5) = 32000 discount gone 32000 x (100/160) = 20000 ... cost.

Yeah I think this is right, I screwed up the 2nd step

Is that rushing sound in my ears just blood or the end of western civilization approaching?

Gameboy is close, but think again on the discount. Instead of 28000*1.125, try 28000/(1-.0125) or 28000/.875. The rest of the calc was right on.

PS - my company sells mostly clothes. 60% would be a terrible markup. Gotta pay for stores, catalogs and people like me to run the numbers.

Slippery wrote:

GameboyRMH wrote: Get rid of the sales tax: (29680/106)*100=28000 Undo the 12.5% discount: 28000*1.125=31500 Lop off Stella's enormous profit margin: (31500/160)*100=19687.50 I really hope that's right, I keep checking it over and I'll feel like a huge moron if it's not.

Lol, this is one of the funniest threads I have seen in a while ... we are all trying to do 13 year old math and cant come up with the same answer. Thanks god I am not homeschooling ... but this is what I got: 29680 x (100/106) = 28000 tax gone 28000 x (100/87.5) = 32000 discount gone 32000 x (100/160) = 20000 ... cost. So diy ... tells us that at least this is multiple choice and you have the answer ... (I am afraid to say that I am an ME ... it might come back and bite me in the ass, lol) J

It's not multiple choice. The answer is $20000. Thanks for the explanation. And the confirmation that I'm terrible at math!

ransom wrote:

dyintorace wrote: So I'm confused even more. To start with, I thought this was the equation to get rid of the tax (hey...at least I thought to do that!). $29680 x .06 = $1780.80 $29680 - $1780.80 = $27899.20

To address these things one at a time, the problem with what you've done above is that the tax is 6% of the retail price, but you've subtracted 6% of the combination of retail price *and* tax. That is, you're subtracting 6% of 106% of the original value... In numbers: 100% * 106% = 106% of the original value 106% * 6% = 6.36% (what you're going to subtract is larger than what you added) 106% - 6.36% = 99.64%

Thanks to your explanation, I see how my formula was wrong.

dyintorace wrote:

Slippery wrote:

GameboyRMH wrote: Get rid of the sales tax: (29680/106)*100=28000 Undo the 12.5% discount: 28000*1.125=31500 Lop off Stella's enormous profit margin: (31500/160)*100=19687.50 I really hope that's right, I keep checking it over and I'll feel like a huge moron if it's not.

Lol, this is one of the funniest threads I have seen in a while ... we are all trying to do 13 year old math and cant come up with the same answer. Thanks god I am not homeschooling ... but this is what I got: 29680 x (100/106) = 28000 tax gone 28000 x (100/87.5) = 32000 discount gone 32000 x (100/160) = 20000 ... cost. So diy ... tells us that at least this is multiple choice and you have the answer ... (I am afraid to say that I am an ME ... it might come back and bite me in the ass, lol) J

It's not multiple choice. The answer is $20000. Thanks for the explanation. And the confirmation that I'm terrible at math!

I was not trying to say that! ... me and my wife were both laughing here because I was not even sure I had it right ... I am glad I did not take all those math classes for nothing!

J

Slippery wrote:

dyintorace wrote:

Slippery wrote:

GameboyRMH wrote: Get rid of the sales tax: (29680/106)*100=28000 Undo the 12.5% discount: 28000*1.125=31500 Lop off Stella's enormous profit margin: (31500/160)*100=19687.50 I really hope that's right, I keep checking it over and I'll feel like a huge moron if it's not.

Lol, this is one of the funniest threads I have seen in a while ... we are all trying to do 13 year old math and cant come up with the same answer. Thanks god I am not homeschooling ... but this is what I got: 29680 x (100/106) = 28000 tax gone 28000 x (100/87.5) = 32000 discount gone 32000 x (100/160) = 20000 ... cost. So diy ... tells us that at least this is multiple choice and you have the answer ... (I am afraid to say that I am an ME ... it might come back and bite me in the ass, lol) J

It's not multiple choice. The answer is $20000. Thanks for the explanation. And the confirmation that I'm terrible at math!

I was not trying to say that! ... me and my wife were both laughing here because I was not even sure I had it right ... I am glad I did not take all those math classes for nothing! J

Don't worry...I wasn't suggesting you were commenting on my (lack of) math knowledge. Moreover, just that even with the way you wrote it out (very logically), I am still a little mystified as to the underlying explanation. I can follow the actual calculations, but never got close to that on my own...even with the answer in hand!

This is not a math problem, it is an ordering problem designed to confuse you. Keep doing them and they get easier.

(Math major)

Real math should never involve percent. 75% should just be written 0.75. 110%? 1.1. Haaaaaate percentages.

Yeah, 20 large:

Let X = price paid.
1.06 * (1.6X-0.125 * 1.6X) =29680
(simplify...)
1.484X=29680
X=20000

I came up with just shy of 18k......but then again, im good with my hands, not math.

Step 1 revenues = sale proceeds * (1 + tax rate)
sale proceeds = revenues / (1 + tax rate)

revenues        29680   
FL tax rate     0.06    
sale proceeds       28000

Step 2 sale proceeds = normal price * (1 - discount rate)
normal price = sale proceeds / (1 - discount rate)

sale proceeds       28000   
discount rate       0.125   
normal price        32000

Step 3 normal price = price paid * (1 + markup)
price paid = normal price / (1 + markup)

normal price        32000   
markup      0.6 
price paid      20000