Question

caitlin won a bag full of money! she has 49 bills in all, she counts $1430. there are twenty dollar bills and fifty dollar bills. how many of each bill does caitlin have? which system best represents the situation?
$\

$$\begin{cases}x + y = 49\\\\20x + 50y = 1430\\end{cases}$$

$
$\

$$\begin{cases}x + y = 49\\\\x + y = 1430\\end{cases}$$

$
$\

$$\begin{cases}x + y = 49\\\\10x + 5y = 1430\\end{cases}$$

$

Explanation:

Step1: Define Variables

Let \( x \) be the number of twenty - dollar bills and \( y \) be the number of fifty - dollar bills.

Step2: Analyze the number of bills

The total number of bills is 49. So the equation for the number of bills is \( x + y=49 \).

Step3: Analyze the total amount of money

Each twenty - dollar bill is worth 20 dollars, so the total value of twenty - dollar bills is \( 20x \) dollars. Each fifty - dollar bill is worth 50 dollars, so the total value of fifty - dollar bills is \( 50y \) dollars. The total amount of money is 1430 dollars. So the equation for the total amount of money is \( 20x + 50y = 1430 \).

Answer:

\(

$$\begin{cases}x + y = 49\\20x+50y = 1430\end{cases}$$

\) (the first system of equations)