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?
That depends upon how long the nonrechargeable batteries last.
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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 buying disposable batteries with the cost of using rechargeable batteries.
First, let's calculate the cost per battery for the disposable option. In a package of 20 batteries for $7.00, the cost per battery is calculated by dividing the total cost by the number of batteries:
Cost per battery = $7.00 / 20 batteries
Next, let's calculate the cost per battery for the rechargeable option. Nathaniel bought 4 rechargeable batteries and a charger for $15.39:
Cost per battery = $15.39 / 4 batteries
Now we can compare the two costs per battery to see which option is cheaper. If the cost per battery for the rechargeable option is lower, it means it's better value and Nathaniel needs to use the rechargeable batteries enough times to be more cost-effective.
Let's do the math:
Cost per battery (disposable) = $7.00 / 20 batteries = $0.35/battery
Cost per battery (rechargeable) = $15.39 / 4 batteries = $3.85/battery
The cost per battery for the disposable option is $0.35, while the cost per battery for the rechargeable option is $3.85. As we can see, the cost per battery for the rechargeable option is significantly higher.
To figure out how many times Nathaniel needs to use the rechargeable batteries to make them a better value, we'll divide the cost per battery for the rechargeable option by the cost per battery for the disposable option:
Number of uses = Cost per battery (rechargeable) / Cost per battery (disposable)
Number of uses = $3.85 / $0.35
Number of uses ≈ 11
Therefore, Nathaniel needs to use each rechargeable battery at least 11 times to make them a better value compared to the disposable batteries.