# Math

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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?

• Math -

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%

• Math -

Oh thanks!

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