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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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3
4
12
70
18
2
30
65
66

1 answer

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

a) Joelle's equation:

  • Joelle currently has 18 rocks and gains 4 each week. The equation will be: \[ y = 4x + 18 \] So the answer for response areas is:
  • Response area for slope: 4
  • Response area for y-intercept: 18

b) Lewis's equation:

  • Lewis currently has 30 rocks and gains 3 each week. The equation will be: \[ y = 3x + 30 \] So the answer for response areas is:
  • Response area for slope: 3
  • Response area for y-intercept: 30

Next, we need to find the number of weeks until Joelle and Lewis have the same number of rocks.

To do this, we set the two equations equal to each other:

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

Solving for \( x \):

  1. Subtract \( 3x \) from both sides: \[ 4x - 3x + 18 = 30 \] \[ x + 18 = 30 \]
  2. Subtract 18 from both sides: \[ x = 30 - 18 \] \[ x = 12 \]

So, the answer for c) is:

  • Response area for weeks: 12 weeks

Finally, we find out how many rocks each will have when they have equal collections. We can substitute \( x = 12 \) into either of the original equations. Using Joelle's equation:

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

So, the answer for d) is:

  • Response area for the number of rocks: 66 rocks

Therefore, the final formatted responses are:

a) Joelle has y = 4x + 18

b) Lewis has y = 3x + 30

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

d) How many rocks will Joelle and Lewis have when the amount of rocks in their collection is equal? They will each have 66 rocks in their collection.