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)%0D%0APut 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.%0D%0Aa) Joelle has y = Response areax + Response area%0D%0A%0D%0Ab) Lewis has y = Response areax + Response area%0D%0A%0D%0Ac) After how many weeks will Joelle and Lewis have the same number of rocks in their collections? Response area weeks%0D%0A%0D%0Ad) 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.%0D%0A%0D%0A186546670231230
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? 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.
wwhat is c and d
c) To determine how many weeks it will take for Joelle and Lewis to have the same number of rocks in their collections, we need to set their equations equal to each other and solve for x:
4x + 18 = 3x + 30
d) To find out how many rocks they will each have in their collection when the amount is equal, we can substitute the value of x into either equation. Let's use Joelle's equation:
y = 4x + 18
Substitute the value of x found in part c
y = 4(week number) + 18
They will each have Response area rocks in their collections.
a) Joelle has y = 4x + 18
b) Lewis has y = 3x + 30
c) To find when Joelle and Lewis have the same number of rocks, we can set their equations equal to each other:
4x + 18 = 3x + 30
d) To find the number of rocks they will each have when their collections are equal, we can substitute the value of x back into one of the equations.
To set up a system of equations to represent the number of rocks Joelle and Lewis have in their collections, we can use the information given.
Let's start with Joelle's collection:
We know that Joelle currently has 18 rocks in her collection and gains 4 rocks each week. So the equation for Joelle's collection can be written as:
y = 4x + 18
Next, let's move on to Lewis's collection:
We know that Lewis currently has 30 rocks in his collection and gains 3 rocks each week. So the equation for Lewis's collection can be written as:
y = 3x + 30
Now, let's answer the questions:
a) Joelle has y = 4x + 18 rocks in her collection.
b) Lewis has y = 3x + 30 rocks in his collection.
c) To find the number of weeks it will take for Joelle and Lewis to have the same number of rocks in their collections, we need to solve the equation 4x + 18 = 3x + 30. Subtracting 3x from both sides, we get x + 18 = 30. Subtracting 18 from both sides gives us x = 12. Therefore, it will take 12 weeks for Joelle and Lewis to have the same number of rocks in their collections.
d) To find the number of rocks Joelle and Lewis will have when the amount of rocks in their collections is equal, we substitute x = 12 into either of the equations. Let's use Joelle's equation:
y = 4(12) + 18
y = 48 + 18
y = 66
Therefore, both Joelle and Lewis will have 66 rocks in their collections when the number of rocks is equal.
Hope this helps! Let me know if you have any further questions.