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) Responses 56=P−4x 56 equals upper P minus 4 x 56=P−3x 56 equals upper P minus 3 x 56=P+4x 56 equals upper P plus 4 x 56=P+3x

Question

GPT-4o mini · Answer

To represent the situation described, we need to set up equations for both Stephanie and Jillian.

For Stephanie:
- She starts with 5 paint bottles and buys 3 new bottles per week. Therefore, after x weeks, her number of paint bottles, P_S, can be expressed as: \[ P_S = 5 + 3x \]
For Jillian:
- She starts with 56 paint bottles and gives away 4 bottles per week. After x weeks, her number of paint bottles, P_J, can be expressed as: \[ P_J = 56 - 4x \]

We are looking for the point in time when both have the same number of paint bottles, meaning: \[ 5 + 3x = 56 - 4x \]

From this, we can rearrange the equation to set it up for comparison. However, regarding the choices given in your question, we want to find the statement that represents Jillian's situation.

From our work, we can derive Jillian's situation into something that looks like this: \[ P = 56 - 4x \] Where P is Jillian's number of paint bottles after x weeks.

Now we analyze the options provided:

56 = P - 4x rearranges to P = 56 + 4x, which does not represent Jillian's situation.
56 = P - 3x does not correspond to either painter.
56 = P + 4x does not represent Jillian's situation.
56 = P + 3x does not represent Jillian's situation.

None of the choices match the correct expressions for either of the painters based on the setup of equations. However, if you meant to have an equation that uses P to denote the count of paint bottles for Jillian, then the correct representation should lead us back to P = 56 - 4x, which can be transformed to 56 = P + 4x for the scenario after rearranging it.

Since the choice "56 = P - 4x" does not reflect the given scenario, it seems the options may not correctly align with the situation presented.

If I assume your values for P and x differently represent Jillian's bottles, then take that option for consideration alternatively. If there are direct rephrases or confusions, please clarify.