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.

Question

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.

Answer 1

a) Joelle has y = 18 + 4x
b) Lewis has y = 30 + 3x
c) To find the number of weeks when they have the same number of rocks, we need to set the two equations equal to each other and solve for x:
18 + 4x = 30 + 3x
x = 12
So after 12 weeks, Joelle and Lewis will have the same number of rocks.
d) To find the number of rocks when they have the same amount, 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
So when the amount of rocks in their collection is equal, they will each have 66 rocks.