Sam the Sham is an unfair shoe salesman. He has a pair of shoes that was priced at $\$60$ last week. To entice customers, he wants to put a "$25\%$ off'' tag on the shoes but he still wants the customer to pay $\$60$ for the shoes. He raises the price of the shoes so that after the $25\%$ discount the shoes will cost $\$60$. In dollars, what must the new price of the shoes be before the discount?
I need to find the new price of the shoes before the discount, which I will call x. I know that after the discount, the shoes will cost $\$60$, which is $75\%$ of x, since the discount is $25\%$ off. So I can write an equation: 0.75x = 60. To solve for x, I need to divide both sides by 0.75. This gives me x = 60 / 0.75. I can use a calculator or long division to find that x = 80. So the new price of the shoes before the discount is $\$80$. 