Question

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 = 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

To set up the system of equations for Joelle and Lewis, we can represent the number of rocks each has as a function of time in weeks.

a) For Joelle:
- She starts with 18 rocks and gains 4 each week.
- The equation representing the number of rocks Joelle has, y, after x weeks is:

**y = 4x + 18**

b) For Lewis:
- He starts with 30 rocks and gains 3 each week.
- The equation representing the number of rocks Lewis has, y, after x weeks is:

**y = 3x + 30**

c) To find out after how many weeks Joelle and Lewis will have the same number of rocks, we set the two equations equal to each other:

\[
4x + 18 = 3x + 30
\]

Now, we can solve for x:

\[
4x - 3x = 30 - 18
\]

\[
x = 12
\]

So, **they will have the same number of rocks after 12 weeks.**

d) To determine how many rocks they will each have when their collections are equal, we can substitute x = 12 back into either equation. We'll use Joelle's equation:

\[
y = 4(12) + 18 = 48 + 18 = 66
\]

Thus, **they will each have 66 rocks in their collection when the amounts are equal.**

To summarize:

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? **12** weeks

d) How many rocks will Joelle and Lewis have when the amount of rocks in their collection is equal? They will each have **66** rocks in their collection.