Question

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?

Answer 1

`\text{The manager has 18 fifty-dollar bills.}`

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:

`20x+50y=1520\text{ (1)}`

She has a total of 49 bills:

`\begin{gathered} x+y=49 \\ x=49-y\text{ (2)} \end{gathered}`

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

`\begin{gathered} 20(49-y)+50y=1520 \\ \end{gathered}`

Solve for y.

`\begin{gathered} 980-20y+50y=1520 \\ 30y=1520-980 \\ y=(540)/(30) \\ y=18\text{ fifty}-\text{dollars} \end{gathered}`