Question 566374
Let {{{n}}} be the number of $1 bills;
let {{{f}}} be the number of $5 bills, and
Let {{{t}}} be the number of $10 bills, as suggested
We start with equations, because some numbers seem to be equal.
We can translate "twice as many tens as fives" as
{{{t=2f}}}
We can translate "four times as many ones than fives" as
{{{n=4f}}} , although I would have stated that as "four times as many ones as fives." 
The total amount of money would be ${{{10t+5f+n}}}, but we can substitute the expressions above to have everything as a function of {{{f}}}, the number of $5 bills.
${{{10t+5f+n}}}=${{{10(2f)+5f+(4f)}}}=${{{20f+5f+4f}}}=${{{29f}}}
So we have ${{{29f}}}.
We know that the amount is "more than $75 but less than $120," so
{{{75<29f<120}}} <--- That's two inequalities in one, but it's OK to write it like this (at least in my book).
So we divide all 3 sides of the inequalities by 29 and get an equivalent double inequality.
{{{75/29<f<120/29}}}
{{{75/29}}} is approximately 2.586 and {{{120/29}}} is approximately 4.138, but {{{f}}} is suposed to be a natural number (a positive integer).
So it could only be {{{f=3}}}, or {{{f=4}}}.
If {{{f=3}}}, the amount of money you have is ${{{29f}}}=${{{29*3}}}=$87.
If {{{f=4}}}, the amount of money you have is ${{{29f}}}=${{{29*4}}}=$116.