A sign above a sweater says “Take an additional 50% off.” The price tag shows a price that is 40% of the regular price. What percent of the regular price is the discounted price (the price after both discounts)?

Question

anonymous · Answer

I think the answer might be 30% I just don't know how to get that answer.

anonymous · Answer

the price is x you would take 40% off then another 50% so total u would take off 90%

anonymous · Answer

so that would leave you 10%

myininaya · Answer

lets think about it.  Say we have something that cost 5 dollars regular price.  If we take 40% off, we get the discount of 2 dollars.  We are now paying 3 dollars for the item.  But there is another discount of 50%.  So the discounted price is is a $1.50.   1.50/5.00=.3=30% is what we are paying. The discount is 70%.

anonymous · Answer

The price would be 20% of the regular price.
Let P = regular price, R = rack price,  F = final price.
$$ R = \frac{40}{100}*P$$
$$ F = \frac{50}{100}*R \rightarrow F= \frac{50}{100}*\frac{40}{100} * P $$
$$= \frac{2000}{10000}*P = \frac{20}{100}*P = \text{20% of the regular price}$$

myininaya · Answer

no its 30% is what we are paying and 70% is the discount I'm 100% sure

myininaya · Answer

x represents the price of an item before any discounts.
the price we are paying is (x-.4x)-[(x-.4x)-.5(x-.4x)]=.3x

myininaya · Answer

the discount price is .7x

myininaya · Answer

So we are paying 30%

anonymous · Answer

$$\text{"40% of the regular price"} \ne \text{"40% off the regular price"}$$

anonymous · Answer

polpak can you help me with a problem when you finish this up...

anonymous · Answer

What problem?

anonymous · Answer

A fence is to be built to enclose a rectangular area of 280 square feet. The fence along three sides is to be made of material that costs 5 dollars per foot, and the material for the fourth side costs 15 dollars per foot. Find the dimensions of the enclosure that is most economical to construct.

anonymous · Answer

Thanks so much Myininaya!! :)