In department and specialty store retailing, a common markup strategy is to double the cost of an item to arrive at the selling price. This strategy is

known as keystoning the markup and is widely used in apparel, cosmetics$,$ fashion accessories, shoes, and other categories of merchandise.

The reasoning for the high amount of markup is that these stores have particularly high operating expenses. In addition, they have a continuing need to

update fixtures and remodel stores to attract customers.

You are the buyer in the women's shoe department of the Roma Grande Department Store. You normally keystone your markups on certain shoes and

handbags. This amount of markup allows you enough gross margin so that you can lower prices when "sales" occur and still have a profitable

department.

$($a$)$ If you are looking for a line of handbags that will retail for $$180,$ what is the most you can pay for the bags $($in $ $)?$

$

$($b$)$ At a women's wear trade show, you find a line of handbags that you like with a suggested retail price of $$170.$ The vendor has offered you trade

discounts of $\frac{25}{20}\frac{?}{9}.$ Will this series of trade discounts allow you to keystone the handbags?

$x,$ because after the trade discounts the cost of each handbag is $

$($c$)($Challenge$)$ The vendor tells you that the first two discounts, $25\%$ and $20\%,$ are fixed, but the $9\%$ is negotiable. What is the minimum trade

discount $($as a $\%),$ rounded to a whole percent, that you should request in order to keystone the markup?

$\%$