Chapter 9, Problem 20CR

To determine

To find the number of bills of each denomination.

Answer to Problem 20CR

The answer is $b.$

  $6$

  $\$1$ , $2$

  $\$5$ and $2$

  $\$10$ bills.

Explanation of Solution

Given:

  $\$36$ has $\$1$ , $\$5$ and $\$10$ bills.

The count of $\$5$ and $\$10$ bills are same

Total count of bills are $10$ .

Calculation:

Given:

  $\$36$ has $\$1$ , $\$5$ and $\$10$ bills.

The count of $\$5$ and $\$10$ bills are same

Total count of bills are $10$ .

Let $\$5$ and $\$10$ bills be $y$ and $\$1$ bill be $x$ .

Thus, we have:

  $\begin{array}{l}x+5y+10y=36\\ x+15y=36\end{array}$

And, $x+2y=10$

  $\begin{array}{l}x+2y=10\\ x=10-2y\end{array}$

Solving the equation $x+15y=36$ for value of $y$ , we have:

  $\begin{array}{l}x+15y=36\\ 10-2y+15y=36\\ 13y=26\\ y=2\end{array}$

Solving the equation $x=10-2y$ for value of $x$ , we have:

  $\begin{array}{l}x=10-2\left(2\right)\\ x=6\end{array}$

Thus, there are $6$

  $\$1$ , $2$

  $\$5$ and $2$

  $\$10$ bills.

Conclusion:

The answer is $b.$

  $6$

  $\$1$ , $2$

  $\$5$ and $2$

  $\$10$ bills.