## To solve the problem "a dozen dozen apples at half a dozen dimes a dozen," we need to break it down step by step:

1. Let's start by clarifying the quantities mentioned:

- A dozen is equal to 12.

- Half a dozen is equal to 6.

- A dime is equal to 10 cents.

2. "A dozen dozen apples" means 12 times 12 apples, which is equal to 144 apples.

3. "Half a dozen dimes a dozen" means 6 times 10 cents (or dimes) times 12 (or a dozen). So, half a dozen dimes a dozen equals 60 cents.

4. Finally, we multiply the number of apples (144) by the price per apple (60 cents) to find the total cost. So, 144 apples multiplied by 60 cents equals $86.40.

Therefore, a dozen dozen apples at half a dozen dimes a dozen would cost $86.40.