For 5 consecutive days, the price of a lamp in jill's store is reduced by 10% from the previous day's price. At the end of the fifth day, by what percetage will the price of the lamp have been reduced from its initial price?

Question

For 5 consecutive days, the price of a lamp in jill's store is reduced by 10% from the previous day's price. At the end of the fifth day, by what percetage will the price of the lamp have been reduced from its initial price?

I'm not sure where to begin since I don't know what the original price of the lamp was. Can you please get me started?

Answer 1

let the original price be $x

after the first discount of 10%, the cost is (.9)x
after the second discount , the cost is (.9)(.9)x = (.9)^2x
after the third discount, the cost is (.9)^3x
.
.
after the 4th discount the cost is (.9)^5x

so percentage of final price to original price is
(.9)^5x/x = .9^5 = .5905 = appr. 59%

so it was reduced by 41%

Answer 2

Oh thanks!

Answer 3

Of course! To solve this problem, we can start by assuming a known initial price for the lamp. Let's say the initial price is $100.

Now, we will calculate the price of the lamp for each of the five consecutive days. On the first day, the price is reduced by 10% of the initial price ($100) which is $10. So, the price of the lamp on the first day is $100 - $10 = $90.

For the subsequent days, the price is reduced by 10% of the previous day's price. So, on the second day, the price is reduced by 10% of $90, which is $9. Therefore, the price of the lamp on the second day is $90 - $9 = $81.

Following the same pattern, the price on the third day is $81 - 10% of $81 which is $8.10, giving us $72.90. Similarly, on the fourth day, the price is reduced by 10% of $72.90, which is $7.29, resulting in $65.61. Finally, on the fifth day, the price is reduced by 10% of $65.61, which is $6.56, making the final price $59.05.

To find the percentage reduction in price from the initial price, we can calculate the difference between the initial price and the final price, divide it by the initial price, and multiply by 100. In this case, it would be:

Percentage reduction = (Initial price - Final price) / Initial price * 100
Percentage reduction = ($100 - $59.05) / $100 * 100
Percentage reduction ≈ 40.95%

So, the price of the lamp will have been reduced by approximately 40.95% from its initial price.