Question

stephanie wants to learn how to paint. she purchases a 5 - pack of paint bottles and buys $3x$ new paint bottles every week. meanwhile, jillian wants to declutter her painting studio. she owns 56 paint bottles and begins to give away 4 paint bottles per week. after $x$ weeks, stephanie and jillian have the same number of paint bottles. create a system of equations in two variables to represent this situation, using $x$ for weeks and $p$ for the number of paint bottles each painter has. which of the following equations belongs to the system? (1 point)
$56 = p + 4x$
$56 = p + 3x$
$56 = p - 4x$
$56 = p - 3x$

Explanation:

Step1: Analyze Stephanie's situation

Stephanie starts with 5 paint bottles and buys \(3x\) new ones every week. So her total number of paint bottles \(P = 5+3x\).

Step2: Analyze Jillian's situation

Jillian starts with 56 paint bottles and gives away 4 per week. So \(56=P + 4x\) (re - arranging gives \(P=56 - 4x\)).

Answer:

A. \(56 = P+4x\)