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.
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.
a) Joelle has y = 18 + 4x
b) Lewis has y = 30 + 3x
c) Set the equations equal to each other and solve for x:
18 + 4x = 30 + 3x
x = 12
After 12 weeks, Joelle and Lewis will have the same number of rocks in their collections.
d) Substitute x = 12 into either equation to find the number of rocks:
y = 18 + 4(12)
y = 18 + 48
y = 66
They will each have 66 rocks in their collection when the amount is equal.
Let's set up the system of equations:
a) Joelle has y = 18 + 4x [Since she has 18 rocks initially and gains 4 rocks each week, the equation represents the total number of rocks (y) she has after x weeks.]
b) Lewis has y = 30 + 3x [Since he has 30 rocks initially and gains 3 rocks each week, the equation represents the total number of rocks (y) he has after x weeks.]
To find the number of weeks it takes for Joelle and Lewis to have the same number of rocks in their collections, we need to set the two equations equal to each other:
18 + 4x = 30 + 3x
To solve this equation, we can subtract 3x from both sides:
18 + x = 30
Next, subtract 18 from both sides:
x = 12
So, after 12 weeks, Joelle and Lewis will have the same number of rocks in their collections.
To find the number of rocks they will each have when the amount in their collections is equal, substitute 12 into either of the original equations:
a) Joelle: y = 18 + 4(12) = 18 + 48 = 66 rocks
b) Lewis: y = 30 + 3(12) = 30 + 36 = 66 rocks
Therefore, when the amount of rocks in their collections is equal, they will each have 66 rocks in their collection.
a) Joelle has y = 18 + 4x, where x represents the number of weeks.
b) Lewis has y = 30 + 3x, where x represents the number of weeks.
c) To find the number of weeks when they have the same number of rocks, we can set their equations equal to each other and solve for x:
18 + 4x = 30 + 3x
Solving for x, we get x = 12.
Therefore, Joelle and Lewis will have the same number of rocks after 12 weeks.
d) To find the number of rocks they will each have at that time, we can substitute x = 12 into either equation:
For Joelle: y = 18 + 4(12) = 66 rocks.
For Lewis: y = 30 + 3(12) = 66 rocks.
Therefore, Joelle and Lewis will each have 66 rocks in their collection when the amount is equal.