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.

how many rocks will Joelle and lewis have when the amount of rocks in their collections is equal

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let's denote Joelle's number of rocks as J and Lewis's number of rocks as L. We can set up the following system of equations:

J = 18 + 4w (J is the number of rocks Joelle has after w weeks)
L = 30 + 3w (L is the number of rocks Lewis has after w weeks)

To find the week when the number of rocks in their collections is equal, we can set J = L and solve the system of equations:

18 + 4w = 30 + 3w

Now, we can solve for w to find the week when the number of rocks in their collections is equal.

Answer 2

okay solve then

Answer 3

[AI-generated answer — Bot GPT 3.5]

18 + 4w = 30 + 3w

To solve for w, we want to isolate the w term on one side of the equation. Let's subtract 3w from both sides:

18 + 4w - 3w = 30 + 3w - 3w

Simplifying:

w = 12

Therefore, after 12 weeks, the number of rocks in Joelle and Lewis's collections will be equal. To find the number of rocks at that time, we can substitute w = 12 into either equation:

J = 18 + 4(12) = 18 + 48 = 66 rocks
L = 30 + 3(12) = 30 + 36 = 66 rocks

So, after 12 weeks, Joelle and Lewis will each have 66 rocks in their collections.

Answer 4

[AI-generated answer — Step-by-Step Bot]

Let's call the number of weeks "w" and the number of rocks in Joelle's collection "J" and in Lewis' collection "L".

Initially, Joelle has 18 rocks, so we can express Joelle's collection as:
J = 18 + 4w

Initially, Lewis has 30 rocks, so we can express Lewis' collection as:
L = 30 + 3w

When the amount of rocks in their collections is equal, we can set J equal to L and solve for w:
18 + 4w = 30 + 3w

Simplifying the equation, we get:
w = 30 - 18
w = 12

Now, substituting the value of w back into either equation to find the number of rocks in their collections will be equal. Let's use Joelle's equation:
J = 18 + 4(12)
J = 18 + 48
J = 66

So, when the amount of rocks in their collections is equal, Joelle and Lewis will each have 66 rocks in their collection.

Answer 5

[AI-generated answer — Explain Bot]

To set up a system of equations for Joelle and Lewis, let's use the variables J and L respectively to represent their number of rocks.

Given that Joelle currently has 18 rocks in her collection and gains 4 each week, the equation for her collection can be represented as: J = 18 + 4w, where w represents the number of weeks.

Similarly, Lewis currently has 30 rocks in his collection and gains 3 each week. So, the equation for his collection can be represented as: L = 30 + 3w.

To find the number of rocks they will have when the amount in their collections is equal, set J equal to L and solve for w:

J = L
18 + 4w = 30 + 3w

Now, solve for w:

4w - 3w = 30 - 18
w = 12

After 12 weeks, Joelle and Lewis will have an equal number of rocks in their collections. To find that number, substitute the value of w back into either equation:

J = 18 + 4(12) = 18 + 48 = 66 rocks
L = 30 + 3(12) = 30 + 36 = 66 rocks

Therefore, both Joelle and Lewis will have 66 rocks in their collection when the amount of rocks in their collections is equal.