Question

pearl wants to invest no more than $2500 into two companies: a fast food chain and a big box store chain. she would like to invest at least 3 times more in the big box store chain than in the fast food chain. if x represents the amount invested in the fast food chain and y represents the amount invested in the big box store chain, what system of inequalities models this situation?\
\\(\

$$\begin{cases}x + y \\leq 2500\\\\y \\geq 3x\\end{cases}$$

\\)\
\\(\

$$\begin{cases}x + y > 2500\\\\y \\geq 3x\\end{cases}$$

\\)\
\\(\

$$\begin{cases}x + y > 2500\\\\y \\leq 3x\\end{cases}$$

\\)\
\\(\

$$\begin{cases}x + y \\leq 2500\\\\y \\leq 3x\\end{cases}$$

\\)

Explanation:

Step1: Analyze total investment limit

The total invested amount $x + y$ cannot exceed $2500$, so:
$x + y \leq 2500$

Step2: Analyze investment ratio requirement

The amount in the big box chain ($y$) is at least 3 times the fast food chain ($x$), so:
$y \geq 3x$

Answer:

$\boldsymbol{x + y \leq 2500}$
$\boldsymbol{y \geq 3x}$
(The first option listed in the question)