instead of buying packages of 20 batteries for $7.00 to power his video game controllers, Nathaniel decides to buy 4 rechargeable batteries and a charger for $15.39. How many times does he need to use the rechargeable batteries to make them a better value?

If he buys x packs of batteries, we wan to find out how many packs it takes to cost more than the price of the charger and batteries.

7x > 15.39
x > 2.2

So, after using the rechargeable batteries 40 times, they will be the better buy.

To determine how many times Nathaniel needs to use the rechargeable batteries to make them a better value, we need to compare the cost of using both the disposable batteries and the rechargeable batteries over time.

First, let's calculate the cost per battery for both options:
- Disposable batteries: $7.00 / 20 batteries = $0.35 per battery
- Rechargeable batteries: $15.39 / 4 batteries = $3.85 per battery

Now, let's assume the rechargeable batteries can be recharged up to 500 times.

To find out how many times Nathaniel needs to use the rechargeable batteries to make them a better value, we can compare the total cost of using both options for the same number of battery uses.

For the disposable batteries:
Number of battery uses = 500 uses
Total cost = Cost per battery * Number of battery uses = $0.35 * 500 = $175.00

For the rechargeable batteries:
Number of battery uses = ?
Total cost = Cost per battery * Number of battery uses + Charger cost
$15.39 = $3.85 * Number of battery uses + Charger cost

Since we don't have the charger cost, let's assume it is a one-time expense and not a significant amount. If we neglect the charger cost for simplicity, the equation becomes:
$15.39 = $3.85 * Number of battery uses

Now, we can solve for the number of battery uses:
Number of battery uses = $15.39 / $3.85 = 4 uses

Therefore, Nathaniel needs to use the rechargeable batteries at least 4 times to make them a better value than the disposable batteries.