Question

The freshman treasury has 30 ten-and twenty-dollar bills That have a total value of $430 dollars. How many of each bill do they have??(Thirty bills in ten and twenty dollar bills)

Answer 1

Let be "t" the number of ten-dollar bills they have and "w" the number of twenty-dollar bills they have.

Using the information given in the exercise, you can set up the following System of Equations:

$\begin{cases}10t+20w=430 \\ t=30-w\end{cases}$

To solve the System of Equations, you can apply the Substitution Method:

1. Substitute the second equation into the first one:

$10(30-w)+20w=430$

2. Solve for "w":

$\begin{gathered} 300-10w+20w=430 \\ 10w=430-300 \\ \\ w=\frac{130}{10} \\ \\ w=13 \end{gathered}$

3. Substitute the value of "w" into the second original equation:

$t=30-(13)$

4. Finally, evaluating, you get:

$t=17$

Therefore, the answer is: They have 17 bills of $10 and 13 bills of $20.