How to get the list price of a tv when a discount has been made?

Question

The problem is as follows:

A seller has made a discount of a $15\%$ from the list price of a tv. Then he makes another discount of 20 usd and still gets a profit of 12 usd. If the cost of that tv was 206 usd. What was the list price of the tv?

The alternatives given in my book are as follows:

$\begin{array}{ll} 1.&\textrm{280 usd}\\ 2.&\textrm{238 usd}\\ 3.&\textrm{216 usd}\\ 4.&\textrm{286 usd}\\ \end{array}$

What I tried to do was as follows: Assuming that the initial price of the tv is $x$.

$x-\frac{15}{100}x-20-206=12$

Solving this yields.

$x=280$

Which I assume is the initial cost of that tv. But is this the right answer?. It would help a lot if an answer could indicate the adequate interpretation of this word problem.

Answer 1

Yes, that is the right answer. Assume that $x$ is the selling price(list price) of the TV. The seller then gives a discount of $15$%, meaning that only $85$% of the price is left, so it becomes $0.85x$ which equals the $x-\frac{15}{100}x$ in your equation. Now, the seller decreases the price by $20$, so the price is now $0.85x-20$. Now, we subtract the expense of the TV to get the profit of $12$, making our equation $0.85x-20-206=12$. Solving, we get $x= 280$, so yes, you are right.