Repeated Discounts. In this exercise, we explore applying more than one discount to an item.

Suppose a store cuts the price on an item by \(50 \%\), and then offers a coupon for \(25 \%\) off any sale item. We will find the price of the item after applying the sale price and the coupon discount.

a. The original price was \(\$ 150\). After the \(50 \%\) discount, what is the price of the item?

b. The coupon is applied to the discount price. The coupon is for \(25 \%\). Find \(25 \%\) of the sale price (found in part a).

c. Find the price after applying the coupon (this is the value from part a minus the value from part b).

d. The total amount saved on the item is the original price after all the discounts. Determine the total amount saved by subtracting the final price paid (part

c) from the original price of the item.

e. Determine the effective discount percentage, which is the total amount saved divided by the original price of the item.

f. Was the effective discount percentage equal to \(75 \%\), which would be the \(50 \%\) plus the \(25 \%\) ? Explain.