oelle currently has 18 rocks in her collection and gains 4 each week. Lewis currently has 30 rocks in his collection and gains 3 each week. Set up a system of equations to show how many rocks each has in their collection.(6 points)Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.a) Joelle has y = Response areax + Response areab) Lewis has y = Response areax + Response areac) After how many weeks will Joelle and Lewis have the same number of rocks in their collections? Response area weeksd) How many rocks will Joelle and Lewis have when the amount of rocks in their collection is equal? They will each have Response area rocks in their collection.436621230186570

Question

oelle currently has 18 rocks in her collection and gains 4 each week. Lewis currently has 30 rocks in his collection and gains 3 each week. Set up a system of equations to show how many rocks each has in their collection.(6 points)Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.a) Joelle has y = Response areax + Response areab) Lewis has y = Response areax + Response areac) After how many weeks will Joelle and Lewis have the same number of rocks in their collections? Response area weeksd) How many rocks will Joelle and Lewis have when the amount of rocks in their collection is equal? They will each have Response area rocks in their collection.436621230186570

Answer 1

Bot GPT 4-o mini answered
2 hours ago

To set up the system of equations for Joelle and Lewis based on the information provided:

Let \( x \) represent the number of weeks.

Joelle's equation:

Joelle starts with 18 rocks and gains 4 each week, so her equation is: \[ y = 4x + 18 \]

Lewis's equation:

Lewis starts with 30 rocks and gains 3 each week, so his equation is: \[ y = 3x + 30 \]

Now, putting the responses in the correct inputs:

a) Joelle has \( y = 4x + 18 \)

b) Lewis has \( y = 3x + 30 \)

To find out after how many weeks Joelle and Lewis will have the same number of rocks:

Set their equations equal to each other: \[ 4x + 18 = 3x + 30 \]

Solving for \( x \):

Subtract \( 3x \) from both sides: \[ x + 18 = 30 \]
Subtract 18 from both sides: \[ x = 12 \]

So, they will have the same number of rocks after 12 weeks.

c) After how many weeks will Joelle and Lewis have the same number of rocks in their collections? 12 weeks

To find out how many rocks they will each have when the amount of rocks in their collection is equal, substitute \( x = 12 \) into either equation. Using Joelle's equation:

\[ y = 4(12) + 18 \] \[ y = 48 + 18 = 66 \]

Using Lewis's equation:

\[ y = 3(12) + 30 \] \[ y = 36 + 30 = 66 \]

So when they have the same number of rocks, they will each have 66 rocks.

d) They will each have 66 rocks in their collection.