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Problem:
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On Tuesday, a radio store reduces all of its prices by 20% from what they were on Monday.
On Wednesday, the store again reduces all of its prices by some percentage from what they were on Tuesday. If the resulting price of a radio is half of the original Monday price,
then by what percentage did the store reduce its prices from Tuesday to Wednesday?

Respuesta :

RevyBreeze

Answer/Step-by-step explanation:

Call Monday's price, P

Tuesday's price must just be .80P   [ 20% reduction]

Call Wednesday's price reduction ( 1 - R)

So...we have that

Tuesday's price  *  Wednesday's reduction  = (1/2)P

(.80)P  *( 1 - R)  = (1/2)P    divide through by  P  and note that 1/2  = .50

.80 (1 - R)  = .50        divide both sides by .80

1 - R  =  .50/.80

1 - R  = 5/8

1 - 5/8 = R

3/8   = R = .375  = 37.5%  = the reduction from Tues. to Wed.

Proof of this...let Monday's price  = 100

Tuesdays price  = .80 * 100   = 80

Wed price  = 80 (1 - R)  = 80 (1 - .375)  = 50 =  half of  Mon. price

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