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.
How many rocks will Joelle and Lewis have when the amount of rocks in their collection is equal? They will each have
Let's represent the number of weeks as "w".
For Joelle, the equation representing the number of rocks in her collection is:
J = 18 + 4w
For Lewis, the equation representing the number of rocks in his collection is:
L = 30 + 3w
To find when the amount of rocks in their collections is equal, we set J = L and solve for w:
18 + 4w = 30 + 3w
Subtracting 3w from both sides:
w = 12
Substituting w = 12 into the equations for Joelle and Lewis:
Joelle will have J = 18 + 4(12) = 18 + 48 = 66 rocks.
Lewis will have L = 30 + 3(12) = 30 + 36 = 66 rocks.
Thus, when the amount of rocks in their collections is equal, they will each have 66 rocks.
Let's represent the number of weeks as "w" and the number of rocks in Joelle's collection as "J" and in Lewis's collection as "L".
According to the given information, Joelle currently has 18 rocks and gains 4 each week. So, the equation for Joelle's collection can be written as:
J = 18 + 4w
Similarly, Lewis currently has 30 rocks and gains 3 each week. So, the equation for Lewis's collection can be written as:
L = 30 + 3w
To find when their collections will have the same number of rocks, we can set J equal to L and solve for w:
18 + 4w = 30 + 3w
Simplifying this equation, we get:
w = 12
Now, we can substitute the value of "w" back into either equation to find the number of rocks when their collections are equal. Let's use Joelle's equation:
J = 18 + 4(12)
J = 18 + 48
J = 66
Therefore, when the amount of rocks in their collection is equal, they will each have 66 rocks.
To set up a system of equations to represent the number of rocks Joelle and Lewis have, we can use the variables J and L to represent their respective collections.
Let's start by representing Joelle's collection. We know that she currently has 18 rocks and gains 4 each week. Therefore, the equation for Joelle's collection can be written as:
J = 18 + 4w
Where w represents the number of weeks that have passed.
Now, let's represent Lewis' collection. We know that he currently has 30 rocks and gains 3 each week. Therefore, the equation for Lewis' collection can be written as:
L = 30 + 3w
To find the number of rocks Joelle and Lewis will have when their collections are equal, we can set J equal to L and solve for w:
18 + 4w = 30 + 3w
Simplifying the equation yields:
4w - 3w = 30 - 18
w = 12
Now that we have the value of w, we can substitute it back into either of the original equations to find the number of rocks each will have at that time. Let's use Joelle's equation:
J = 18 + 4w
J = 18 + 4(12)
J = 18 + 48
J = 66
Therefore, when the number of rocks in their collections is equal, each will have 66 rocks.