Question 1154912
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            I will make you surprised.


            I will solve the problem using only one single unknown.


            Watch my steps (!)



<pre>
Let x be the number of the 5-dollar bills.

Then the number of the 10-dollar bills is (x+2), according to the condition.

Next, the one-dollar bills are the rest  (35 - x - (x+2)) = 33 - 2x  banknotes.


Now, I write the total money equation


    1*(33-2x) + 5x + 10*(x+2) = 144.


Next, I simplify it


    33 - 2x + 5x + 10x + 20 = 144

    -2x + 5x + 10x = 144 - 33 - 20

     13x           = 91

       x           = {{{(91)/(13)}}} = 7.


<U>ANSWER</U>.  7 (seven) 5-dollar bills;  7+2 = 9 10-dollar bills  and  the rest  35 - 7 - 9 = 19 one-dollar bills.


<U>CHECK</U>.  7*5 + 9*10 + 19*1 = 144.      ! Precisely correct !
</pre>

Solved.


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This problem, and many hundreds similar problems, are designed, are destined and are expected to be solved 

by 6-7 grade students, who don't know any systems of equations, and who need to be touched/(to be trained) on 

how to solve them (the problems) using one single equation in one single unknown.


It is why such problems are/were created, at all.



To see many other similar solved problems, look into the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/coins/More-complicated-coin-problems.lesson>More complicated coin problems</A>


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/equations/More-complicated-word-problems-to-solve-using-single-linear-equation.lesson>More complicated word problems to solve using a single linear equation</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/equations/Advanced-word-problems-to-solve-by-reduction-to-single-linear-equation.lesson>Advanced word problems to solve using a single linear equation</A>

in this site.