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.

a) Joelle has y = Response x + Response

b) Lewis has y = Response x + Response

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]

a) Joelle has y = 18 + 4x (where x represents the number of weeks)

b) Lewis has y = 30 + 3x (where x represents the number of weeks)
c) To find when Joelle and Lewis have the same number of rocks, we set their equations equal to each other: 18 + 4x = 30 + 3x
d) To find how many rocks they have when the amount is equal, we can solve the equation.

Answer 2

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

a) Joelle has y = 18 + 4x

b) Lewis has y = 30 + 3x

c) To find the number of weeks when Joelle and Lewis have the same number of rocks, we need to equate their equations:

18 + 4x = 30 + 3x

Simplifying the equation, we get:

x = 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 their collections are equal, we substitute x = 12 into either equation:

Joelle: y = 18 + 4(12)
= 18 + 48
= 66 rocks

Lewis: y = 30 + 3(12)
= 30 + 36
= 66 rocks

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

Answer 3

[AI-generated answer — Explain Bot]

a) Joelle has y = 18 + 4x, where x represents the number of weeks.

Explanation: Joelle currently has 18 rocks in her collection, and she gains 4 rocks each week. We represent the number of weeks as x. Therefore, the equation for Joelle's collection would be y = 18 + 4x, where y represents the number of rocks in her collection.

b) Lewis has y = 30 + 3x, where x represents the number of weeks.

Explanation: Lewis currently has 30 rocks in his collection, and he gains 3 rocks each week. Similar to Joelle, we represent the number of weeks as x. Therefore, the equation for Lewis's collection would be y = 30 + 3x, where y represents the number of rocks in his collection.

c) To determine the number of weeks for Joelle and Lewis to have the same number of rocks, we set their equations equal to each other:

18 + 4x = 30 + 3x

Explanation: We are trying to find the point at which both Joelle and Lewis have the same number of rocks in their collections. By setting their equations equal to each other, we can find the value of x (number of weeks) that satisfies this condition.

d) To determine the number of rocks Joelle and Lewis will have when their collections are equal, we substitute the value of x into either equation:

Using 18 + 4x:

Rocks in Joelle's collection = 18 + 4x
Rocks in Lewis's collection = 18 + 4x

Explanation: Since x represents the number of weeks, we substitute the value of x into either Joelle's or Lewis's equation to find the number of rocks in their collections when they have the same quantity. Both individuals will have the same number of rocks in their collections.