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

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.

• Looks OK to me. Your equation expresses the profit realized by the seller as a function of the inputs. There are equivalent ways of formulating the problem but all of them would get there. Mar 4, 2021 at 5:00

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.