Samuel currently has 18 rocks in his collection and gains 4 each week. Lewis currently has 30 rocks in his collection and gains 3 each week.

Question

Part A: Set up a system of equations to show how many rocks each has in their collection. You must write two equations for this. (2 points)

Part B: After how many weeks will Samuel and Lewis have the same number of rocks in their collections? Write out the equation used and show all work. (1 point)

Part C: How many rocks will Samuel and Lewis have when the amount of rocks in their collection is equal? Show work on how this is found. (1 point)

Answer 1

Part A:

Let x be the number of weeks passed.

Samuel: y = 18 + 4x
Lewis: z = 30 + 3x

Part B:

We want to find when y and z are equal, so we set up an equation:

18 + 4x = 30 + 3x

Simplify:

x = 12

So after 12 weeks, Samuel and Lewis will have the same number of rocks.

Part C:

To find the number of rocks they will have when the amount is equal, we can substitute x = 12 into either equation.

y = 18 + 4(12) = 66

So Samuel will have 66 rocks.

z = 30 + 3(12) = 66

So Lewis will also have 66 rocks.