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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) a) Joelle has y b) Lewis has y = weeks = x +! c) After how many weeks will Joelle and Lewis have the x +¦ same number of rocks in their collections? each have d) How many rocks will Joelle and Lewis have when the amount of rocks in their collection is equal? They will rocks in their collection.
a) Joelle's collection: y = 18 + 4x
b) Lewis's collection: y = 30 + 3x
c) To find the number of weeks when they have the same number of rocks, we set their collections equal to each other: 18 + 4x = 30 + 3x
d) To find the number of rocks each will have when their collections are equal, substitute the number of weeks (x) into either equation.
a) Joelle has y rocks in her collection.
b) Lewis has y = x + 30 rocks in his collection, where x represents the number of weeks.
c) To find the number of weeks when Joelle and Lewis have the same number of rocks, we need to solve the equation y = x + 30 = 18 + 4x, where y represents the number of rocks in their collections.
d) To find the number of rocks they will have when they have equal amounts, we can plug in the number of rocks (y) into either equation and solve for x.
To set up a system of equations to represent the number of rocks each person has in their collection, we can use the given information.
Let's define:
- Joelle's number of rocks as J
- Lewis's number of rocks as L
a) Joelle has 18 rocks in her collection and gains 4 each week.
This can be represented by the equation: J = 18 + 4x, where x is the number of weeks.
b) Lewis has 30 rocks in his collection and gains 3 each week.
This can be represented by the equation: L = 30 + 3x, where x is the number of weeks.
c) To find the number of weeks after which Joelle and Lewis have the same number of rocks in their collections, we set J and L equal to each other:
18 + 4x = 30 + 3x
d) To find the number of rocks they each have when the amount is equal, we can substitute the number of weeks obtained from part c) into either equation (J or L) and solve for the number of rocks.