A shoe store offers a 30% discount on the list price x of a particular item. The cashier then discounts the price by another 15%.

Question

1. Evaluate P(D(50)) and interpret its meaning.
2. Solve P(D(x)) = 100.

Answer 1

Two possible interpretations. Both roughly the same

x=50

30% discount then 15% discount

P(D(x)) =.85(.7)x

D(x) =.7x

P(D(x)) = .85(.7)x = .595x

P(D(50)) =.595x = the fully discounted price after two discounts of 30 and 15%

P(D(50)) = .595(50) = $29.75 = fully discounted Price on an original price of $50

P(D(x)) =100 = .595x

x = 100/.595 = $168.07 = original Undiscounted price rounded to nearest penny

30% off leaves 70% or .7(168.07) = $117.65

another 15% off leaves 85% or .85(117.65) = $100

UNLESS the 2nd discount was off the original price and not the first discounted price

then

30+15=45% off leaving 55% of the original price as the discounted price

P(D(x)) = .55x

P(D(50)) = .55(50) = $27.50 as the discounted price

P(D(x))=100=.55x

x =100/.55 = $181.82 = Original Price, rounded to nearest cent