QuestionA customer believes increasing a price by $20\%$ and then decreasing it by $20\%$ returns it to the original price. Is this true?

Studdy Solution

STEP 1

Assumptions1. The original price of the item is $$. . The price of the item is increased by $20\%$.
3. Then, the increased price is decreased by $20\%$.
4. The customer believes that the final price will be equal to the original price.

STEP 2

First, we need to calculate the new price after the item's cost is increased by $20\%$ . We can do this by multiplying the original price by $1$ plus the percentage increase (expressed as a decimal).
$New\, price = \times (1 + Percentage\, increase)$

STEP 3

Now, plug in the given value for the percentage increase to calculate the new price.
$New\, price = \times (1 +20\%)$

STEP 4

Convert the percentage to a decimal value.
$20\% =0.2$ $New\, price = \times (1 +0.2)$

STEP 5

Calculate the new price.
$New\, price = \times1.2$

STEP 6

Now, we need to calculate the final price after the new price is decreased by $20\%$ . We can do this by multiplying the new price by $1$ minus the percentage decrease (expressed as a decimal).
$Final\, price = New\, price \times (1 - Percentage\, decrease)$

STEP 7

Now, plug in the given value for the percentage decrease to calculate the final price.
$Final\, price = \times1.2 \times (1 -20\%)$

STEP 8

Convert the percentage to a decimal value.
$20\% =0.2$ $Final\, price = \times1.2 \times (1 -0.2)$

STEP 9

Calculate the final price.
$Final\, price = \times.2 \times.8$

STEP 10

implify the expression.
$Final\, price = \times0.96$ From this, we can see that the final price is $96\%$ of the original price, not $100\%$ . Therefore, the customer's belief is incorrect. The final price will not return to its original price after an increase of $20\%$ and a decrease of $20\%$ .

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