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)
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a) Joelle has y = x +
b) Lewis has y = x +
c) After how many weeks will Joelle and Lewis have the same number of rocks in their collections? weeks
d) How many rocks will Joelle and Lewis have when the amount of rocks in their collection is equal? They will each have rocks in their collection.
a) Joelle has y = 18 + 4x
b) Lewis has y = 30 + 3x
c) After how many weeks will Joelle and Lewis have the same number of rocks in their collections? weeks
d) How many rocks will Joelle and Lewis have when the amount of rocks in their collection is equal? They will each have 102 rocks in their collection.
a) Joelle has y = 18 + 4x
b) Lewis has y = 30 + 3x
c) To find the number of weeks it takes for Joelle and Lewis to have the same number of rocks, we need to set their equations equal to each other:
18 + 4x = 30 + 3x
Now, we can solve for x. Subtracting 3x from both sides:
18 + x = 30
Subtracting 18 from both sides:
x = 12
So, it will take 12 weeks for Joelle and Lewis to have the same number of rocks in their collections.
d) To find how many rocks Joelle and Lewis will have when the amount of rocks in their collection is equal, we substitute x = 12 into either of their equations:
Joelle: y = 18 + 4(12) = 18 + 48 = 66 rocks
Lewis: y = 30 + 3(12) = 30 + 36 = 66 rocks
Therefore, they will each have 66 rocks in their collection when the amount is equal.
a) Joelle has y = 18 + 4x
b) Lewis has y = 30 + 3x
c) To find the number of weeks when Joelle and Lewis have the same number of rocks, we need to set their equations equal to each other and solve for x:
18 + 4x = 30 + 3x
Subtracting 3x from both sides, we get:
x = 12
Therefore, they will have the same number of rocks after 12 weeks.
d) To find the number of rocks they will have when the amount is equal, we can substitute x = 12 into either equation:
Joelle: y = 18 + 4(12) = 18 + 48 = 66 rocks
Lewis: y = 30 + 3(12) = 30 + 36 = 66 rocks
Therefore, they will each have 66 rocks in their collection when the number of rocks is equal.