jeweler math question. if you know how to do it id appreciate it!?

Question

a jeweler sells all of his merchandise for double what it costs him, but he charges no sales tax. instead, he pays the sales tax out of his profits. a woman comes in to buy a ring and notices a scratch on the band. the jeweler takes 1/4 off the price and sells the ring for $159.99. what was the jeweler's final profit if the tax is 20%?

Answer 1

With this scratched band, he sold it for $159.99, which is after the 25% discount. So, his original cost was $159.99/75% (since $159.99 represents 3/4 of the original price), or $213.32. If you need an equation, follow this (with x being his initial selling price):

x * 0.75 = 159.99
x = 159.99/0.75
x = 213.32

Thus, his initial cost is half of this, or $106.66.

Taxes on the final sale come to $159.99 * 20%, or $32. So if his final sale price was $159.99, and he spent $32 on tax and $106.66 initially, his final profit is $21.33.