Question

let x represent the number of pens manufactured and let y represent the number of mechanical pencils manufactured. choose the system that best models this situation.
o x + y = 400
1.25x + 0.5y = 500
o x + y = 500
1.25x + 0.5y = 400
o x + y = 500
0.5x + 1.25y = 400
o x - y = 500
1.25x - 0.5y = 400

Explanation:

Step1: Set up equations based on problem

Let \(x\) be number of pens and \(y\) be number of mechanical pencils. Total number of items manufactured is \(x + y\). If total number of items is 500, we have \(x + y=500\). Cost - related equation: cost per pen is \(1.25\) and per mechanical pencil is \(0.5\), and total cost - related amount is 400, so \(1.25x+0.5y = 400\).

Answer:

\(1.25x + 0.5y=400\), \(x + y = 500\) (corresponding to the option where these two - equations are paired)