Posted by april on Friday, August 28, 2009 at 6:34pm.
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.