**Martha's millinery sold two evening gowns at the same price. Based on their cost, the store made 25% on one of the gowns and lost 25% on the other. As a result of these transactions, what was the percentage gain or loss?**

Here is the original solution I found on: *Algebra.com*: https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1124792.html

However, the problem is, the solution is too vague, and skips multiple steps near the end. Can someone help clarify this problem, from the beginning?

Thanks!

MathyGoo13 Oct 2, 2022

#1**-1 **

1 - Sold at $100 which includes a profit of 25%

Therefore, the cost of the 1st gown ==$100 /1.25 **==$80**

2 - Sold at $100 which includes a loss of 25%

Therefore, the cost of the 2nd gown==$100 / [1 - 0.25]==$100 / 0.75 **==$133.33**

3 - The total cost of the 2 gowns==$80 + $133.33**==$213.33**

4 - Income received from the sale of the 2 gowns==$100 + $100 **==$200**

5 - Loss in dollar terms==$213.33 - $200 **==$13.33**

6 - Loss as percentage of cost**==$13.33 / $213.33 ==~6.25%**

Guest Oct 2, 2022

#3**0 **

The selling price was not 1.25x or 0.75x, it was the ending cost because if they made "25%" off of one of the gowns, the profit would've been 25$, the starting price wouldn't have been 1.25x... That's a logic flaw...

proyaop
Oct 3, 2022

#4**+1 **

*The selling price was not 1.25x or 0.75x, it was the ending cost because if they made "25%" off of one of the gowns, the profit would've been 25$, the starting price wouldn't have been 1.25x... That's a logic flaw...*

**Proyaop, there is no logical error in the question or Mr. BB’s solution.**

Note the question:

Martha's millinery sold two evening gowns at __the same price__. __Based on their cost__, the store made 25% on one of the gowns and lost 25% on the other. ...

The gowns sell at the same price. The profit and loss is based on the (store’s) costs for the gowns.

So, Mr. BB’s nonstandard (slop) presentation depicts the correct solution.

GA

--. .-

GingerAle
Oct 3, 2022

#2**+2 **

I would try to generalize the cost of the gowns with a variable, say --- "g"!

A 25% increase is 1.25 (1 + 25/100), so the final cost of one of the gowns would be 1.25g.

A 25% decrease is 0.75 (1 - 25/100), so the final cost of the other gown would be 0.75g.

Adding these two together, it gets 2g, which also happens to be the original cost of both:

Thus, as the result of these transactions, **the percentage gain/loss = 0%**

proyaop Oct 3, 2022

#5**+1 **

Solution:

\(\mathrm G_1 = \text {cost of gown 1}\\ \mathrm G_2 = \text {cost of gown 2 }\\ \text {Arbitrary sale price } $100 \\ ---\\ \mathrm G_1 + 0.25G_1 = 100 \\ 4(\mathrm G_1) + \mathrm G_1 = 400 \\ \mathrm 5G_1 = 400 \\ \mathrm G_1 = 80 \\ ---- \\ \)

\(G_2 + (-.025G_2) = 100 \\ 4(G_2) = - G_2 = 400 \\ 3G_2 = 400 \\ G_2 = 133.33 \\ \text {Total cost for gowns } = 213.33\\ \text {Revenue from sale }= 200.00 \\ \text {P/(L) } = (13.33)\\ \text {P/(L)%} = (1-(200/213.33)) \rightarrow (6.25\%) \text { Loss}\\ \)

**Solution (without the use of an arbitrary sale price):**

**\(\mathrm G_1 + 0.25\mathrm G_1 = \mathrm G_2 - 0.25\mathrm G_2\\ 4\mathrm G_1 + \mathrm G_1 = 4\mathrm G_2 - \mathrm G_2 \\ 5\mathrm G_1 = 3\mathrm G_2 \\ \mathrm G_1 = 3/5\mathrm G_2 \\ \mathrm G_1 = 0.60\mathrm G_2 \\ --- \\ \mathrm G_1 \text { must equal 60% of the cost of } \mathrm G_2\\ \text {Or } \\ \mathrm G_2 \text { must equal 167% of the cost of } \mathrm G_1\\ \)**

GA

--. .-

GingerAle
Oct 3, 2022