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.

c) After how many weeks will Joelle and Lewis have the same number of rocks in their collections? Response 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 rocks in their collection.

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let's call the number of weeks "w".

Joelle's equation: 18 + 4w
Lewis's equation: 30 + 3w

To find the number of weeks when they have the same number of rocks, we need to set their equations equal to each other and solve for "w".

18 + 4w = 30 + 3w

Subtract 3w from both sides:
18 + w = 30

Subtract 18 from both sides:
w = 12

So Joelle and Lewis will have the same number of rocks in their collections after 12 weeks.

To find how many rocks they will each have at that time, we can substitute 12 for "w" in either equation. Let's use Joelle's equation:

18 + 4(12) = 18 + 48 = 66

So they will each have 66 rocks in their collections when the amount of rocks is equal.

Answer 2

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

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

According to the information given, Joelle currently has 18 rocks in her collection and gains 4 each week. So, the equation to represent the number of rocks in Joelle's collection would be:
J = 18 + 4w ------- (equation 1)

Similarly, Lewis currently has 30 rocks in his collection and gains 3 each week. So, the equation to represent the number of rocks in Lewis' collection would be:
L = 30 + 3w ------- (equation 2)

c) To find out after how many weeks Joelle and Lewis will have the same number of rocks in their collections, we need to find the value of "w" when J = L. So, we can set equation 1 equal to equation 2 and solve for "w":
18 + 4w = 30 + 3w

By simplifying the equation, we get:
w = 12

Therefore, after 12 weeks, Joelle and Lewis will have the same number of rocks in their collections.

d) To find out how many rocks Joelle and Lewis will have when the amount in their collections is equal, we substitute the value of "w" (which is 12) into either equation 1 or equation 2. Let's use equation 1:
J = 18 + 4 * 12
J = 18 + 48
J = 66

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

Answer 3

[AI-generated answer — Explain Bot]

To set up a system of equations, we'll use the information given in the question.

Let's denote the number of weeks as "w."
Joelle currently has 18 rocks in her collection and gains 4 each week. So, the number of rocks Joelle will have after "w" weeks can be represented by the equation:
J(w) = 18 + 4w

Lewis currently has 30 rocks in his collection and gains 3 each week. So, the number of rocks Lewis will have after "w" weeks can be represented by the equation:
L(w) = 30 + 3w

Now, let's solve the system of equations to answer the given questions.

c) After how many weeks will Joelle and Lewis have the same number of rocks in their collections?
To find the number of weeks, we need to find the value of "w" for which J(w) = L(w). So, we can set up the equation:
18 + 4w = 30 + 3w

Solving this equation will give us the value of "w" when Joelle and Lewis have the same number of rocks.

d) How many rocks will Joelle and Lewis have when the amount of rocks in their collection is equal?
To find the number of rocks, we need to find the common value of J(w) and L(w). So, we can set up the equation:
18 + 4w = 30 + 3w

Solving this equation will give us the number of rocks they will each have when their collections are equal.