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Problem of the Week
Problem B
When is This Deal a Deal?

Danielle uses a battery-powered magnifying headlamp when creating silver jewellery. The headlamp requires one AA battery.

Instead of buying a \(10\)-pack of non-rechargeable AA batteries for \(\$17.50\), she decides to buy one rechargeable battery and a charger for \(\$40\).

Suppose each non-rechargeable battery is used until it no longer works and the rechargeable battery is used until it needs to be recharged. Also suppose that the length of time until a non-rechargeable battery no longer works is the same as the length of time until a rechargeable battery needs to be recharged.

After how many rechargeable battery uses will Danielle’s choice be a better deal than buying \(10\)-packs?

You may find the table below to be useful. For example, after \(5\) uses of the rechargeable battery, the price per use for the rechargeable battery will be \(\$40\div 5 = \$8.00\).

Number of Rechargeable Battery Uses Price Per Rechargeable Battery Use
\(5\) \(\$8.00\)


Theme: Number Sense