stuck on ratios proportions percentages, any work/explanation added in answer would be greatly appreciated.
a store sells an item it originally marked up 30% of the cost price, at a discount of 58% of the selling price. What percent of the cost is the resulting profit or loss on this sale?

Question

stuck on ratios proportions percentages, any work/explanation added in answer would be greatly appreciated. 
a store sells an item it originally marked up 30% of the cost price, at a discount of 58% of the selling price. What percent of the cost is the resulting profit or loss on this sale?

anonymous · Answer

or if someone can direct me to the section of this site that has similar questions or is in a subtopic that would help, I am new to this site. Thanks

solomonzelman · Answer

This is a good section for this question, it's math and the question has to do with math.

I can help you, but Iidk what they mean by
30% of the cost price, at a discount of 58% of the selling price.

solomonzelman · Answer

I meant to say, what do they mean by MARKED UP 30 percent...

anonymous · Answer

I believe it means the store got the item for a certain price and sells it at 30% more, then the reduced selling price is 58% less than the price that it was selling at which was the 30% on top of the price they bought it at. I'm not sure how to formulate the equations for that

directrix · Answer

Let $1 be the cost of the item.

Then, the 30% mark-up selling price is $1.30.

The $1.30 item is now sold at a  discount of 58% of the selling price.

So, the $1.30 item is sold for $1.30 - .58($1.30) = $.546 which would be 55 cents.

So, approx 55 cents is the selling price of the 30% marked up item.

The question asks this:

 What percent of the cost is the resulting profit or loss on this sale?

The cost is $1.00. The discounted item was sold for $.546 so the percent of the cost which is lost is $1.00 - $.546. = $.453 or 45.3%.

--------------------
Algebraically,

Let x = the cost of the item.

Then, the 30% mark-up selling price is 1.3x

The $1.3*x item is now sold at a  discount of 58% of the selling price.

So, the $1.3*x item is sold for $1.3*x - .58($1.3x) = $.546x.

The item cost is x. The item sold for .546x. 

 What percent of the cost is the resulting profit or loss on this sale?

x - .546x = .454x or 45.4% loss on the sale.

@danielleo

anonymous · Answer

Thank you so much! That explanation helped me work through some of my other problems as well

directrix · Answer

Glad to help @danielleo .