Joe currently has 18 rocks in her collection and gains 4 each week Louis currently has 30 rocks in his collection and gains 30 each week after how many weeks would Joel and Louis have the same number of rocks in their collection?
Let's say after x weeks, Joe will have 18 + 4x rocks.
Louis will have 30 + 30x rocks after x weeks.
If they have the same number of rocks after x weeks, then:
18 + 4x = 30 + 30x.
Rearranging the equation, we get:
4x - 30x = 30 - 18.
-26x = 12.
Dividing both sides by -26, we get:
x = -12/-26 = 0.46(approximately).
So, it would take approximately 0.46 weeks for Joe and Louis to have the same number of rocks in their collection.
To determine the number of weeks it would take for Joel and Louis to have the same number of rocks in their collection, we need to set up and solve an equation. Let's denote the number of weeks as 'w'.
For Joel's collection:
Starting with 18 rocks, the number of rocks after 'w' weeks is given by the equation: 18 + 4w.
For Louis's collection:
Starting with 30 rocks, the number of rocks after 'w' weeks is given by the equation: 30 + 30w.
Setting the two equations equal to each other, we have:
18 + 4w = 30 + 30w
Simplifying the equation, we get:
4w - 30w = 30 - 18
-26w = 12
Dividing both sides by -26, we have:
w = -12 / -26
w = 0.46 (approximately)
Since 'w' represents the number of weeks, we round up to the nearest whole number. Thus, it would take approximately 1 week for Joel and Louis to have the same number of rocks in their collection.
To find out after how many weeks Joel and Louis would have the same number of rocks in their collection, we need to set up an equation based on their current number of rocks and weekly gains.
Let's suppose the number of weeks needed is represented by "w".
For Joel:
Number of rocks = 18 + 4w
For Louis:
Number of rocks = 30 + 30w
To find the point of intersection, where their collections would be equal, we set these two expressions equal to each other:
18 + 4w = 30 + 30w
Simplifying the equation:
4w - 30w = 30 - 18
-26w = 12
Divide both sides by -26:
w = 12 / -26
w ≈ -0.4615
Since the number of weeks cannot be negative or fractional, we can conclude that Joel and Louis will never have the same number of rocks in their collection.