Dylan brought his DVD set of The Sleuth in the Shadows Saga to a secondhand store to sell. He was paid cash for all 4 DVDs in the set. Before he left, Dylan used $16.40 of his earnings to purchase a backpack. He had $3.60 remaining. How much did Dylan receive for each DVD in the set?
$
Dylan received a total of $16.40 + $3.60 = $<<16.40+3.60=20>>20 for the 4 DVDs.
Each DVD in the set sold for $20 / 4 DVDs = $<<20/4=5>>5. Answer: \boxed{5}.
Let's assume Dylan received x dollars for each DVD in the set.
He had 4 DVDs, so the total amount he received for selling the DVDs can be calculated as 4x.
Out of this total amount, he used $16.40 to purchase a backpack, so he was left with 4x - $16.40.
According to the given information, he had $3.60 remaining, so we can write the equation:
4x - $16.40 = $3.60
Adding $16.40 to both sides of the equation:
4x = $3.60 + $16.40
Simplifying:
4x = $20
Dividing both sides of the equation by 4:
x = $20 / 4
x = $5
Therefore, Dylan received $5 for each DVD in the set.
To find out how much Dylan received for each DVD in the set, we can use algebra. Let's represent the unknown amount Dylan received for each DVD as "x".
Since Dylan sold 4 DVDs in total, the total cash he received can be calculated by multiplying the number of DVDs sold (4) by the amount received for each DVD (x). This can be written as:
4x = Total cash received
After purchasing the backpack, Dylan had $3.60 remaining. If we subtract the cost of the backpack ($16.40) from the total cash received, it should equal the remaining amount. This can be written as:
Total cash received - Cost of backpack = Remaining amount
4x - $16.40 = $3.60
Now we can solve this equation to find the value of x, which represents how much Dylan received for each DVD.
4x - $16.40 = $3.60
4x = $3.60 + $16.40
4x = $20.00
To isolate x, we divide both sides of the equation by 4:
4x / 4 = $20.00 / 4
x = $5.00
Therefore, Dylan received $5.00 for each DVD in the set.