A convention manager finds that she has $1,520, made up of twenties and fifties. She has a total of 49 bills. How many fifty-dollar bills does the manager have?

Respuesta :

Answer:

[tex]\text{The manager has 18 fifty-dollar bills.}[/tex]

Step-by-step explanation:

To solve this situation we can create a system of equations with the given information.

Let x be the number of twenties

Let y be the number of fifties.

If she has a total of $1,520:

[tex]20x+50y=1520\text{ (1)}[/tex]

She has a total of 49 bills:

[tex]\begin{gathered} x+y=49 \\ x=49-y\text{ (2)} \end{gathered}[/tex]

Then, substitute equation (2) into equation (1):

[tex]\begin{gathered} 20(49-y)+50y=1520 \\ \end{gathered}[/tex]

Solve for y.

[tex]\begin{gathered} 980-20y+50y=1520 \\ 30y=1520-980 \\ y=\frac{540}{30} \\ y=18\text{ fifty}-\text{dollars} \end{gathered}[/tex]