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

How many rocks will Joelle and Lewis have when the amount of rocks in their collection is equal? They will each have

Answer 1

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.