In evaluating the selling prices for products at her part$-$time retail job, Hecharim asked his supervisor how the company sets its prices. His supervisor told him it applies a steady markup percentage on each product$$s cost$.$ He selected a lightweight jacket off the rack and noted its selling price of $$100.$ His supervisor looked at the selling price and then told Hecharim that the gross margin percentage is $60\%.$ What markup percentage on cost is the company using to set its selling price? If the company instead used a $75\%$ markup percentage on cost$,$ what would the selling price have been?