# High school Math team questions!!

After successive discounts of 25%, 20%, 37.5% and 33(1/3)% are applied to the original price of an item, the final price of that item is the same as if the original price had been discounted once by n%. Compute n. Is the answer 66.625. If not, please teach me how to approach to the right answer!! Thank you very much!!!

• This is easier if you calculate the reduced prices (instead of just the discounts), and then translate the final answer to a discount at the end. – John Joy Oct 26 '14 at 20:29

Lets call the original amount $A$. Then, after the first discount the price would become:$$A\times(1-0.25)=a\times0.75$$The second discount should now be applied to this new amount so after the second discount the price would become:$$A\times0.75\times(1-0.2)=A\times0.75\times0.8=A\times0.6$$This means that the first two discounts are equivalent to $(1-0.6)=0.4=40$%. Keep applying this rule until you end up with something like:$$A\times r$$The equivalent discount is then $(1-r)\times100$%