Joe currently has 18 rocks in her collection and gains 4 each week. Louis currently has 30 rocks in his collection and gains three each week how many rocks with Joe and Lewis have when the amount of rocks in their collection is equal
We can set up the equation: 18 + 4w = 30 + 3w, where w represents the number of weeks.
Subtract 3w from both sides: 18 + w = 30.
Subtract 18 from both sides: w = 12.
Therefore, Joe and Louis will have the same number of rocks after 12 weeks.
To calculate the total number of rocks, we can substitute w with 12 in either equation.
Joe will have 18 + 4(12) = 18 + 48 = 66 rocks.
Louis will have 30 + 3(12) = 30 + 36 = 66 rocks.
Therefore, Joe and Louis will each have 66 rocks when the amount of rocks in their collection is equal.
To find out how many rocks Joe and Louis will have when the amount of rocks in their collection is equal, we need to set up an equation.
Let's assume it will take "x" weeks for the amount of rocks in their collections to be equal.
Joe's collection after "x" weeks: 18 + 4x
Louis's collection after "x" weeks: 30 + 3x
Since we want to find the number of rocks when their collections are equal, we can set up the equation:
18 + 4x = 30 + 3x
To solve for "x," let's subtract 3x from both sides of the equation:
18 + x = 30
Next, subtract 18 from both sides:
x = 12
So, it will take 12 weeks for the number of rocks in their collections to be equal.
Now, let's substitute this value back into one of the equations to find the number of rocks they will each have at that time.
Using Joe's equation: 18 + 4x
Substituting x = 12, we get:
18 + 4(12) = 18 + 48 = 66
Thus, Joe and Louis will each have 66 rocks when the amount in their collections is equal.
To find out how many rocks Joe and Louis will have when the number of rocks in their collection is equal, we can set up an equation.
Let's assume the number of weeks it takes for the collections to be equal is represented by 'x'.
Joe currently has 18 rocks and gains 4 each week, so the equation for Joe's collection is:
Joe's rocks = 18 + 4x
Louis currently has 30 rocks and gains 3 each week, so the equation for Louis' collection is:
Louis' rocks = 30 + 3x
To find the point at which their collections are equal, we can set these equations equal to each other:
18 + 4x = 30 + 3x
To solve for 'x', we need to isolate the 'x' term on one side of the equation. Let's subtract 3x from both sides to achieve this:
18 + 4x - 3x = 30
Combining like terms, we have:
x = 30 - 18
x = 12
So, it will take 12 weeks for Joe and Louis' collections to be equal.
To determine the number of rocks they will have at that time, substitute this value of 'x' back into either of the equations:
Joe's rocks = 18 + 4x
Joe's rocks = 18 + 4(12)
Joe's rocks = 18 + 48
Joe's rocks = 66
Therefore, at that point, both Joe and Louis will have 66 rocks in their collections.