Question

Question

Joelle 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 area

b) Lewis has y = Response areax + Response area

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

d) 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.

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Answer 1

To set up the system of equations based on the given information:

1. Joelle's collection:

   • Joelle starts with 18 rocks and gains 4 rocks each week.
   • Let \( x \) be the number of weeks.
   • The equation for Joelle's rocks is: \[ y = 4x + 18 \]

2. Lewis's collection:

   • Lewis starts with 30 rocks and gains 3 rocks each week.
   • The equation for Lewis's rocks is: \[ y = 3x + 30 \]

Now, let's fill in the responses based on these equations:

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

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

Next, to find out after how many weeks Joelle and Lewis will have the same number of rocks, we need to set their equations equal to each other:

\[ 4x + 18 = 3x + 30 \]

Now, solve for \( x \):

\[ 4x - 3x = 30 - 18 \] \[ x = 12 \]

c) After 12 weeks, Joelle and Lewis will have the same number of rocks.

Finally, we substitute \( x = 12 \) back into either equation to find out how many rocks they will each have at that time:

Using Joelle's equation: \[ y = 4(12) + 18 = 48 + 18 = 66 \]

Using Lewis's equation: \[ y = 3(12) + 30 = 36 + 30 = 66 \]

Thus, they will each have 66 rocks.

d) They will each have 66 rocks in their collection when their amounts are equal.

To summarize:

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

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

c) After 12 weeks.

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