Samantha saved $13 by buying a used DVD. She paid $5 less than half the original price of a new one. How much did Samantha pay for a used DVD?

Solve the problem backwards.

She paid $5 less than half the original price.

So add $5 to what she paid would be half the original price.

I'm sure you can take it from here.

To find out how much Samantha paid for the used DVD, let's break down the information and work step by step.

1. We are told that Samantha saved $13 by buying a used DVD.
2. We are also told that she paid $5 less than half the original price of a new one.

Let's represent the original price of the new DVD as "x." According to the second piece of information, Samantha paid $5 less than half of x, which can be expressed as:

(1/2)x - $5

Now, we know that Samantha saved $13, so we can set up the following equation:

x - [(1/2)x - $5] = $13

Let's solve this equation to find the value of x, which is the original price of the new DVD.

x - (1/2)x + $5 = $13

Multiplying through by 2 to eliminate the fraction, we get:

2x - x + 10 = 26

Simplifying further, we have:

x + 10 = 26

Subtracting 10 from both sides:

x = 16

So, the original price of the new DVD was $16.

Now, we can calculate how much Samantha paid for the used DVD. We were told she paid $5 less than half of the original price, which can be calculated as:

(1/2) * $16 - $5

= $8 - $5
= $3

Therefore, Samantha paid $3 for the used DVD.