Calculate the Final Price: Air Conditioner’s Cost After 10% Increase and 15% Decrease

Question

The price of an air conditioner is 2500 dollars. At the beginning of the summer season, its price increased by 10% and at the end of the season its price decreased by 15%.

What is the price of the air conditioner at the end of the season?

Video Solution

Solution Steps

00:00 Determine the final price
00:08 Determine the price after summer inflation
00:24 Convert from percentages to fractions, and multiply by the original price
00:37 Break down 2500 into factors of 25 and 100
00:42 Reduce wherever possible
00:51 This is the discount that needs to be added to the original price
01:10 This is the price after the summer inflation
01:15 Now let's calculate 15 percent of this price
01:28 Convert from percentages to fractions, and multiply by the price
01:38 Break down 2750 into factors of 55 and 50
01:43 Break down 100 into factors of 50 and 2
01:53 Reduce wherever possible
02:09 Subtract the discount from the summer price and calculate to find the price
02:32 This is the solution

Step-by-Step Solution

To solve this problem, we will walk through each step sequentially:

  • Step 1: Calculate the price after a 10% increase.

  • Step 2: Calculate the price after a 15% decrease from the increased price.

Now, let's work through these steps:
Step 1: The original price of the air conditioner is \2500 \). When the price is increased by 10%, the new price is calculated as follows: New price after 10% increase=2500×(1+10100)=2500×1.10=2750 \text{New price after 10\% increase} = 2500 \times \left(1 + \frac{10}{100}\right) = 2500 \times 1.10 = 2750

Step 2: This increased price of \2750isthendecreasedby15Final price after 15% decrease=2750×(115100)=2750×0.85=2337.52750 is then decreased by 15%. The new price after this decrease is calculated by:</p><p><span class="katex">\( \text{Final price after 15\% decrease} = 2750 \times \left(1 - \frac{15}{100}\right) = 2750 \times 0.85 = 2337.5

Therefore, the price of the air conditioner at the end of the season is 2337.5 2337.5 dollars.

Answer

2337.5 $