My daughter was given this problem in her homework, and we're having a hard time figuring it out. Hopefully, someone here can help.

A shoe store marks up the price of it's shoes 120% over cost. A pair of shoes goes on sale for 20% off, and then goes on the clearance rack for an additional 30% off. A customer walks in with a 10% off coupon good on all clearance items, and buys the shoes. Express the store's profit on these shoes as a percentage of the original cost.

We have the answer, but we don't know how to figure it out.

We're thinking

(0.9)(0.8)(0.7)B (where B is the base price of the shoes, .9, .8 and .7 represent 10% off, 20% off and 30% off, respectively). Where does the 120% come in?

Can anyone help?

quote:

Originally posted by 4x5:
My daughter was given this problem in her homework, and we're having a hard time figuring it out. Hopefully, someone here can help.

A shoe store marks up the price of it's shoes 120% over cost. A pair of shoes goes on sale for 20% off, and then goes on the clearance rack for an additional 30% off. A customer walks in with a 10% off coupon good on all clearance items, and buys the shoes. Express the store's profit on these shoes as a percentage of the original cost.

We have the answer, but we don't know how to figure it out.

We're thinking

(0.9)(0.8)(0.7)B (where B is the base price of the shoes, .9, .8 and .7 represent 10% off, 20% off and 30% off, respectively). Where does the 120% come in?

Can anyone help?

I think the only piece you are missing is the original price which is 2.2B, so
2.2B(.9)(.8)(.7)

Store buys shoes for $50, marks it up 120% so that is retail $110 ((50*1.2)+50)

On sale 20% off is $110-22= $88.

Another 30% off $88-(88*.3)= $61.60 is the selling price so 61.60/50 which is 23.2% of cost.

Forgot the 10% coupon! $61.60-6.16 = $55.44 so 5.44/50 is 10.88%.

After discounts, I'm getting 10.88% profit

quote:

Originally posted by Rebel-22:

quote:

Originally posted by 4x5:
My daughter was given this problem in her homework, and we're having a hard time figuring it out. Hopefully, someone here can help.

A shoe store marks up the price of it's shoes 120% over cost. A pair of shoes goes on sale for 20% off, and then goes on the clearance rack for an additional 30% off. A customer walks in with a 10% off coupon good on all clearance items, and buys the shoes. Express the store's profit on these shoes as a percentage of the original cost.

We have the answer, but we don't know how to figure it out.

We're thinking

(0.9)(0.8)(0.7)B (where B is the base price of the shoes, .9, .8 and .7 represent 10% off, 20% off and 30% off, respectively). Where does the 120% come in?

Can anyone help?

I think the only piece you are missing is the original price which is 2.2B, so
2.2B(.9)(.8)(.7)

I tried that earlier, but must have messed up something, because now using that equation I get the right answer. Thanks!

it's 10.88%

What did the customer pay?

What was the store's cost?

Divide one by the other.

I think the part that puzzles people is the 120% markup...people are seeing that but are thinking 20%.

quote:

Originally posted by lkdr1989:
I think the part that puzzles people is the 120% markup...people are seeing that but are thinking 20%.

I got the 2.2 for 120%, but don't really understand why or how. I know 100% markup is 2x, but.....yeah.

Basically. (B+ 1.2B)(.9)(.8)(.7) = 2.2B(.9)(.8)(.7) = 1.1088B since 1B is the cost then markup is 1.1088-1 = .1088 = 10.88%

Ken

" Express the store's profit on these shoes as a percentage of the original cost."

The question asks for the percentage, not an equation used to determine the percentage, so it's easier to plug in a number and go through the sequence of mark up and discounts from there.

I recommend JALLEN's method, except that I think it's easier to start w/ a number such as $10 or $100.

Thanks everyone! My daughter appreciates the help

Same

JB

quote:

Originally posted by lkdr1989:
After discounts, I'm getting 10.88% profit

quote:

Originally posted by lkdr1989:
After discounts, I'm getting 10.88% profit

Profit Margin is not the same as Markup, which represents how the price of an offer compares to its total cost.

Here’s the formula for Markup:
((Price - Cost) / Cost) * 100 = % Markup

If the cost of an offer is $1 and you sell it for $2, your markup is 100%.

Here is the formula for Profit Margin:
((Revenue - Cost) / Revenue) * 100 = % Profit Margin

Margins can never be more than 100 percent, but Markups can be 200 percent, 500 percent, or 10,000 percent, depending on the price and the total cost of the offer.

The higher your price and the lower your cost, the higher your Markup.

~~~~~~~~~~~~~~~~~~~~~~

C for Cost $1
M for Markup 120%

OP for Original Price = $C + ($C*M%) = $2.20
SP for 20% Sale Price = $OP - ($OP*20%) = $1.76
CP for 30% Clearance Price = $SP - ($SP*30%) = $1.23
CD for 10% Coupon Discount = $CP - ($CP*10%) = $1.11

M for Markup = ((Price - Cost) / Cost) * 100 = (($1.11 - $1) / $1 * 100 = 10.88%
"Express the store's profit on these shoes as a percentage of the original cost."

~~~~~~~~~~~~~~~~~~~~~~

If you need the final price as one formula:
P for final Price =
(((($C + ($C * M%)) * SP%) * CP%) * CD%) = Price
(((($1 + ($1 * 120%)) * 80%) * 70%) * 90%) = $1.11

In the first set of formulas, I used
$OP - ($OP*20%) = $1.76 to show the 20% off. But I could have used:
$OP * 80% = $1.76 which is still 20% off but you use 80% in the formula.
Remember 80% + 20% = 100%

In the combined formula, I used the 80% to make it cleaner...

This message has been edited. Last edited by: sleepla8er,

Although I agree with the math folks have presented, I think the original problem is ambiguous. It says the shoes go on sale for 20% off and then to the Clearance rack for "an additional 30% off". Responders have been applying the new 30% discount to the price created by the original 20% discount, but I read "additional 30%" as referring to the original 20%, yielding a combined Clearance aisle discount of 50%. If that were the case, using $50 as the cost; the original price would have been $110; after the first 20% discount the price would be $88; on the Clearance rack it would be $55; and with the customer's discount of 10% ($5.50) would be $49.50. The store would have lost 50 cents on the shoes. This is a loss of 1%.

I don't know that this is the correct answer, but it is a possible interpretation of the original problem statement.

flashguy

quote:

Originally posted by flashguy:
...It says the shoes go on sale for 20% off and then to the Clearance rack for "an additional 30% off".

Responders have been applying the new 30% discount to the price created by the original 20% discount, but I read "additional 30%" as referring to the original 20%, yielding a combined Clearance aisle discount of 50%...
flashguy

If FlashGuy is correct, then....

C for Cost $1
M for Markup 120%

OP for Original Price = $C + ($C * M%) = $2.20
SP for 20% Sale Price = $OP - ($OP * 20%) = $1.76
CP for 20% + 30% Clearance Price = $OP - ($OP * 50%) = $1.10
CD for 10% Coupon Discount = $CP - ($CP * 10%) = $0.99

M for Markup = ((Price - Cost) / Cost) * 100 = (($0.99 - $1) / $1 * 100 = -1%
"Express the store's profit on these shoes as a percentage of the original cost."

quote:

Originally posted by 4x5:

quote:

Originally posted by lkdr1989:
I think the part that puzzles people is the 120% markup...people are seeing that but are thinking 20%.

I got the 2.2 for 120%, but don't really understand why or how. I know 100% markup is 2x, but.....yeah.

Original cost is x, the markup alone, ie the price on top of the cost is 1.2x (120%). For the total original price, it'll be original cost x + markup 1.2x = 2.2x.

If cost were $100, then the markup would be 120 bucks. They'd sell it for $220.

If the shoes originally cost $100 pair, but then marked up 120%, then marked down by 20% followed by another 30% markdown and then a 10% further markdown, the price of the shoes would be

(100 + 1.2 * 100) * .8 * .7 * .9 == 110.88

The store's profit margin would then be (110.88 -100) or 10.88%.

I agree with flashguy. The way that the problem is stated, it is not clear whether additional discounts are taken from the original price or from the current discounted price.

If I were the teacher I would give extra credit to any student(s) who pointed this out and gave solutions for both interpretations.

Others have covered the correct answer.
My answer is 20 based on OP's screen name.

My head hurts. I'll stick to chasing bad guys.

There's a reason I flunked Calc, twice...