An item in a store will bemarked up 30% tomorrow, and then will be discounted 40

Question

An item in a store will bemarked up 30% tomorrow, and then will be discounted 40% fromtomorrow's price the day after tomorrow. If the storeowner wants toapply one single discount equivalent to these two chnages, whatpercent discount would that be? I know the answer is 52% but i don't know how i got to theanswer. Plz show me how i could actually reach the answer. Pleaseshow all the work. An item in a store will bemarked up 30% tomorrow, and then will be discounted 40% fromtomorrow's price the day after tomorrow. If the storeowner wants toapply one single discount equivalent to these two chnages, whatpercent discount would that be? I know the answer is 52% but i don't know how i got to theanswer. Plz show me how i could actually reach the answer. Pleaseshow all the work.

Explanation / Answer

. 0.01.   A price that ismarked-up by a percentage of the current price is equivalentto adding the percentage of the current price to the... current price. If the price of the item is 'a' andit is marked-up 10% then its marked-up price is: 0.02.   (a) + (10%)*(a) = (a)+ (0.1)*(a) ==> factoring "a" ==> (a)*(1.0 + 0.1) =(a)*(1.1) 0.03.   A price that isdiscounted by a percentage of the current price is equivalent tosubtracting the percentage of the current price from thecurrent price. If the price of the item is 'b' and it isdiscounted 10% then its discounted price is: 0.04.   (b) - (10%)*(b) = (b)- (0.1)*(b) ==> factoring "b" ==> (b)*(1.0 - 0.1) =(b)*(0.9) 0.05.   If I want to find theequivalent of these two actions--a mark-up followed by adiscount--I just need to discount the marked-up price. Ergo... 0.06.   c = equivalentpercentage mark-up or discount ; using the 10% mark-up followed bythe 10% discount (see above) 0.07.   c = [(a)*(1.1)]*(0.9)= (a)*(1.1)*(0.9) = (a)*(0.99) = (a)*(99%) 0.08.   Thus, what ever theoriginal item cost (the value of 'a'), at the end of the mark-upand discount activity the new value of 'a' is 99% of what it wasbefore the activity.
0.09.   Numerically, assume thata0=$342.00. The mark-up value wouldbe: 0.10.   a1 =(a0)*(1.1) = ($342.00)*(1.1) = $376.20   when I discount a1 the value becomes: 0.11.   a2 =(a1)*(0.9) = ($376.20)*(0.9) =$338.58   but we know from the above thata2 is equivalent to 99% of a0==> 0.12.   a2 =(a0)*(0.99) = ($342.00)*(0.99) = $338.58 . 1.   Let's assume the "item" costs $100.00. 2.   If it is marked-up by 30% tomorrow, then thenew price is: 3.      New Price = ($_item) +($_item)*(0.30) = ($_item)*(1 + 0.30) = ($100.00)*(1.3) =$130.00 . 4.   If the item is then discounted by 40%, then thenew price is: 5.      New Price = ($_item) -($_item)*(0.40) = ($_item)*(1 -0.40) = ($130.00)*(0.6) =$78.00 . 6.   Therefore, the equivalent discount for thesetwo changes would be: (1+0.3)*(1-0.4) = 0.78 = 78% . 7.   P.S. If the 2nd discount was 60%rather than 40% the equivalent discount would be: (1+0.3)*(1-0.6) = 0.52 = 52%

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