+0

# percents...

+1
1186
5
+4618

A merchant offers a large group of items at 30% off. Later, the merchant takes 20% off these sale prices and claims that the final price of these items is 50% off the original price. As a percentage of the original price, what is the difference between the true discount and the merchant's claimed discount?

Apr 16, 2018

#1
0

Let the original average price of one item =\$100

\$100 x 0.7 =\$70 - price after 30% original discount.

\$70 x 0.8 =\$56 - price after the 2nd 20% discount.

\$100 - \$56 =\$44 - The final amount of discount after the 30% and 20% sale.

\$44 / \$100 =0.44 x 100 =44% - the true discount compared to the mercant's claim.

Apr 16, 2018
#2
+4618
+1

Sorry, but that's incorrect.

Apr 16, 2018
#3
+129829
+2

Call the original price of the goods, P

After a 30% discount   the price is .7P

And...after a 20% discount on this the final price is  (.7P) (.8)  = .56P

So...the discount  is just [ P  -.56P]  = .44P

And the merchant's claimed discount is .50P

So....the difference between the true discount and merchant's claimed discount  is

l  .44P - .50P  l   =  l  -.06P l  =   .06P   =  [ 6 %  of the original price ]

Apr 16, 2018
#4
+4618
+1

Thanks so much, CPhill!

tertre  Apr 16, 2018
#5
+1356
+10

Good job CPhill!!

Apr 16, 2018