SOLUTION: By selling a dress for $5500, a woman lost 30%. For how much should she have sold it to gain 30%

Question 1150818: By selling a dress for $5500, a woman lost 30%. For how much should she have sold it to gain 30%
Found 3 solutions by greenestamps, Theo, MathTherapy:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Selling with a 30% loss means the selling price was 70% of the cost.

Selling with a 30% gain means the selling price would be 130% of the cost.

If a price of $5500 is 70% of the cost, then 130% of the cost is

which to the nearest dollar is $10214.

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
she sold the dress for 5500 and lost 30%.

let c equal the cost of the dress.
let s equal the price she sold it at.
let p equal the profit she sold it at.
a negative profit is the same as a loss.

equation to use is:

p = (s - c) / c
when p = -30%, then p = -.30
you use the rate, not the percent.
this becomes:
-.30 = (5500 - c) / c
multiply both sides of this equation by c to get:
-.30 * c = 5500 - c
add c to both sides of this equation to get:
c - .30 * c = 5500
combine like terms to get:
.70 * c = 5500
solve for c to get:
c = 5500 / .7 = 7857.142857

to confirm, take 30% off 7857.142857 and you get 5500.
5500 is what it sold at when 30% was lost.

to gain 30%, use the same equation.

p = (s - c) / c

when p = 30% and when c = 7857.142857, then the equation becomes:

.3 = (s - 7857.142857) / 7857.142857
once again, you use the rate, not the percent.
multiply both sides by 7857.142857 to get:
.3 * 7857.142857 = s - 7857.142857
add 7857.142857 to both sides of the equation to get:
.3 * 7857.142857 + 7857.142857 = s
solve for s to get:
s = 10214.28571

to confirm, add 30% to 7857.142857 and you get 10214.28571
this is what it sells at when 30% is gained.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

By selling a dress for $5500, a woman lost 30%. For how much should she have sold it to gain 30%

Losing 30% means that itw's sold for 70%, or .7, which is actually $5,500
We then get the following PROPORTION, with selling price to gain 30%, being P:
.7P = 1.3(5,500) ------ Cross-multiplying
P, or selling price in order to gain 30% =
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