Final answer:
To restore the original price of a coat after a 10% reduction, we must increase the new price by 11.11%, because the original and new base prices differ after the reduction.
Step-by-step explanation:
If the price of a coat is reduced by 10%, to restore it to its original price, we should not increase it by the same percentage because the base has changed. Instead, if we call the original price 100%, after a 10% decrease, the new price is 90% of the original. To find the percentage increase to get back to the original, we set up the equation 90% + (90% × x) = 100%, where x is the percentage increase needed. Solving for x gives us 0.9x = 0.1, or x = 11.11%. So, to restore the original price, we need to increase the new price by 11.11%.