Suppose the price of a $185 item increases by 11.7%. By what percent does the resulting price have to decrease in order for the final price (after the two changes) to be back to the original price of $185?
(185 * 1.117) * ? = 185 ... ? = 1 / 1.117 = 0.895 = 1 - .105
10.5% decrease
To find the percent decrease needed for the final price to be back to the original price, we need to work step by step.
Step 1: Calculate the increase in price.
The price of the item increases by 11.7%.
11.7% of $185 = (11.7/100) * $185 = $21.645.
Step 2: Calculate the new price.
The original price is $185 and it increases by $21.645.
New price = Original price + Increase = $185 + $21.645 = $206.645.
Step 3: Calculate the decrease needed to get back to the original price.
The final price needs to be equal to the original price of $185.
Difference = New price - Original price = $206.645 - $185 = $21.645.
Step 4: Calculate the percent decrease needed.
Percentage decrease = (Difference / New price) * 100
= ($21.645 / $206.645) * 100
≈ 10.46%.
Therefore, the resulting price would need to decrease by approximately 10.46% in order for the final price to be back to the original price of $185.