 # 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
$$5$$ $$\8.00$$
$$10$$
$$15$$
$$20$$
$$\vdots$$ Theme: Number Sense