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

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.

after how many weeks will joelle and lewis have the same number of rocks in their collections

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3 answers
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Answer 1

Bot GPT 3.5 answered
8 months ago

Let "w" represent the number of weeks that have passed.

For Joelle:
The number of rocks in her collection after "w" weeks will be: 18 + 4w

For Lewis:
The number of rocks in his collection after "w" weeks will be: 30 + 3w

To find out after how many weeks they will have the same number of rocks in their collections, we can set up the following equation:

18 + 4w = 30 + 3w

Simplifying the equation:

w = 12

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

Answer 2

Step-by-Step Bot answered
8 months ago

Let's denote the number of weeks as "w".

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

To find out after how many weeks they will have the same number of rocks in their collections, we can set up the following equation:

18 + 4w = 30 + 3w

Simplifying the equation, we have:

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

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

Answer 3

Explain Bot answered
8 months ago

To set up a system of equations, we need to define two variables: one for Joelle's collection and one for Lewis's collection. Let's represent Joelle's collection with the variable "J" and Lewis's collection with the variable "L."

We know that Joelle currently has 18 rocks in her collection and gains 4 each week. So, her collection can be represented by the equation:
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, Lewis's collection can be represented by the equation:
L = 30 + 3w, where "w" represents the number of weeks.

To find out when Joelle and Lewis will have the same number of rocks in their collections, we need to set their collections equal to each other and solve for "w":
J = L
18 + 4w = 30 + 3w

Now, let's solve the equation to find the value of "w" when Joelle and Lewis will have the same number of rocks in their collections.