A dollar that costs a dollar

February 12, 2014

I had one of those awesome experiences this week where a student thinks of a better question.

I had been playing around with this issue of what money costs to make. Not a pretty picture, by the way. Rounding only a little for simplicity and age appropriateness, we had this chart of costs:

Penny: 2.5 cents

Nickel: 11 cents

Dime: 6 cents

Quarter: 11 cents

My question was, what coin makes the cheapest dollar, and what coin makes the most expensive dollar? (For example, a dollar in dimes would cost 60 cents to make.) There was some controversy as kids staked some initial claims, and then everyone set to work.

But one girl ignored my question in favor of her own, which I have to say, is straight up better: can you make a dollar in coins that also costs a dollar to make? The dollar in dimes costs only 60 cents. What about eight dimes, two nickels, and ten pennies? As you can check, that costs 95 cents to make. So close!

And here’s the even better sequel to the story. This same girl worked with incredible focus for the next thirty-five minutes, and answered her own question. Can you find how she did it? Is there more than one answer?

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