Assuming that the treasury has a total of 30 bills with values of 10 and 20 dollars and that the total value is 430. We have:
[tex]\begin{gathered} x+y=30 \\ 10\cdot x+20\cdot y=430 \end{gathered}[/tex]Where x is the number of 10 dollar bills and y is the number of 20 dollar bills. We can multiply the first equation by -10 and then add the two equations to solve for y.
[tex]\begin{gathered} -10x-10y=-300 \\ 10x+20y=430 \\ 20y-10y=430-300 \\ 10y=130 \\ y=13 \end{gathered}[/tex]We can replace "y" with 13 on the first equation to determine the value of "x".
[tex]\begin{gathered} x+13=30 \\ x=30-13 \\ x=17 \end{gathered}[/tex]The total of 10 dollar bills is 17, while the total of 20 dollar bills is 13.
