Elizabeth has $10, $5, and $1 bills worth $101. she has five more five dollar bills than ten dollar bills and 4 times more 1 dollar bills than 10 dollar bills. How many of each kind of bills does elizabeth have?

Let F = The number of $5 bills and T = the number of $10 bills.  She has 15 bills total, so:

F+T = 15                

T = 15-F

She has $120 total:

$120 = ($5)*F + ($10)*T

$120 = $5*F + ($10)*(15-F)         [Substitute 15-F in place of T]

120 = 5F + 150 - 10F

-30 = -5F

6 = F

Check:

T= 15-F = 15=6 = 9

$120 = ($5)*6 + ($10)*9

$120 = $30 + $90

$120 = $120