91Ó°ÊÓ

There are total $54$bills of $$10$and $$20$.

The total value of the money is localid="1658886804935" $\$910$.

We need to find the number of $$10$ and $$20$ bills.

Let $x$represents the number of $$10$ bills

and $y$represents the number of $$20$ bills.

The total number of bills is $54$, so the equation is

$x+y=54...\left(1\right)$

Now, the total amount is $$910$where $x$is the number of $$10$bills and $y$is the number of $$20$bills. So the equation is

$10x+20y=910...\left(2\right)$

Solve the first equation for $y$

$\begin{array}{rcl}x+y& =& 54\\ x+y-x& =& 54-x\\ y& =& 54-x...\left(3\right)\end{array}$

Using the third equation substitute $54-x$for $y$in the second equation and solve for $x$

$\begin{array}{rcl}10x+20y& =& 910\\ 10x+20(54-x)& =& 910\\ 10x+1080-20x& =& 910\\ 10x-20x+1080-1080& =& 910-1080\\ -10x& =& -170\\ x& =& 17\end{array}$

Substitute $17$for $x$in the third equation

$$\begin{gathered} y=54-x \\ y=54-17 \\ y=37 \end{gathered}$$

Thus the number of $$10$bills is $17$and the number of $$20$bills is $37$.

Substitute $17$for $x$and $37$for $y$in the first equation formed.

$\begin{array}{rcl}x+y& =& 54\\ 17+37& =& 54\\ 54& =& 54\end{array}$

It is a true statement.

Again, substitute the values in the second equation formed.

$\begin{array}{rcl}10x+20y& =& 910\\ 10·17+20·37& =& 910\\ 170+740& =& 910\\ 910& =& 910\end{array}$

This is also a true statement.

So the point satisfies both the equations.