math word problem
posted by april .
chris has twice as many 1 dollar bills as pennies he has twice as many dimes as he has 10 dollar bills he has twice as many pennies as he has dimes how much money does chris have?

let the number of pennies be x
"chris has twice as many 1 dollar bills as pennies"
> $1  2x
"he has twice as many pennies as he has dimes"
> dimes  x/2
"he has twice as many dimes as he has 10 dollar bills"
> $10  x/4
value of his money in pennies:
x + 10(x/2) + 100(2x) + 1000(x/4)
= x + 5x + 200x + 250x
= 456x pennies
There is no unique answer, but we can argue as follows:
for the variables x, 2x, x/2 and x/4 we must have positive whole numbers, so the smallest value of x possible is 4
so he could have
one $10 bill
2 dimes
8 $1 bills and
4 pennies for a total of $18.24
or x = 8, then he would have $36.48 etc. 
There is not enough information to give a numerical answer.
Let t=number of ten dollar bills.
"he has twice as many dimes as he has 10 dollar bills", so the amount A is
A=10*t+0.1*(2t)
"he has twice as many pennies as he has dimes"
A=10*t+0.1*(2t)+0.01*4t
"chris has twice as many 1 dollar bills as pennies"
A=10*(t)+0.1*(2t)+0.01*(4t)+1*(8t)
=18.24t
Therefore the total amount Chris has is 18.24 times the number of $10 bills he possesses.
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