Question 415294: The number of nickels, dimes, and quarters in a bank are consecutive odd integers, in increasing order. If there are d dimes, what is the value of the money in cents?
I have no idea if I am over thinking the question or not but do I have to convert everything to cents first and then solve in terms of that? Nickels are 0.5 dimes, and quarters 2.5 dimes. Consecutive odd integers mean nickels are our base valuje: (0.5d)5, dimes 10(d+2), and quarters are 25(2.5d+4)?????
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the problem says there are d dimes.
since they want the answer in cents, it makes sense to use cents.
a nickel is worth 5 cents
a dime is worth 10 cents
a quarter is worth 25 cents
the problem states that you have d dimes.
the number of dimes is therefore equal to d.
the problem states that the number of coins is in consecutive odd integer order.
they don't really tell you which is first and which is next and which is next after that.
i would think the order would be nickels, dimes, quarters, but it's not clear from the problem.
assuming that there are d dimes, and assuming the order is nickels, dimes, quarters, then the money in the bank would be equal to:
5*(d-2) + 10*d + 25*(d+2)
a basic assumption would have to be that d is greater than or equal to 3.
another basic accumption would have to be that d is always odd.
assume d = 3, then the formula would be:
5 * 1 + 10*3 + 25*5 = 5 + 30 + 125 = 160 cents.
if we combine like terms in the formula of:
money in the bank = 5*(d-2) + 10*d + 25*(d+2), we would get:
money in the bank 40*d + 40
when d = 3, the amount of money would be equal to 120 + 140 = 160 cents.
40*d + 40 is equivalent to 5*(d-2) + 10*d + 25*(d+2)
take another value of d, like 33 (a nice odd number.
40*33 + 40 = 1360 cents.
5 * (31) + 10 * 33 + 25 * 35 = 155 + 330 + 875 = 1360 cents.
you get the same number any way.
converting nickels to equivalent dimes to equivalent quarters wasn't necessary.
converting everything to cents up front was better.
also, since your problem stated there were d dimes, you needed to get equivalent nickels and quarters using the number of dimes as the base.
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