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 Question from vicky, a student: Chris has twice as many $1 bills as pennies, twice as many dimes as he has$10 bills, and twice as many pennies as he has dimes. How much money does he have?

Hi Vicky,

When I looked at this I got a pencil and wrote what is given using symbols to shorten what I had to write. I let T for the number of ten dollar bills Chris had, D for the number of dimes, P for the number of pennies and L for the number of one dollar bills. (I had already used D for dimes and I am in Canada where we have a one dollar coin we call a loonie, hence the L.). The three statements you have are

Chris has twice as many $1 bills as pennies: L = 2P twice as many dimes as he has$10 bills: D = 2T
twice as many pennies as he has dimes: P = 2D

From this you can see that if you know T you can find D and from D you can find P and then L. You didn't give any other restriction so it looks like I can choose T to be anything I want. For example it T = 1 then D = 2, P = 4 and L = 8. Similarly if T = 5 then D = 10, P = 20 and L = 40. In fact you might have T = 0 and then D = P = L = 0 and poor Chris is broke.

Do you have any other information?
Penny

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