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.
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)
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.
Part A: Let's denote the number of weeks as 'w'.
The number of rocks in Samuel's collection can be represented by the equation:
S = 18 + 4w
The number of rocks in Lewis' collection can be represented by the equation:
L = 30 + 3w
Part B: To find out when Samuel and Lewis will have the same number of rocks, we need to set their equations equal to each other:
18 + 4w = 30 + 3w
Simplifying the equation, we get:
w = 12
So after 12 weeks, Samuel and Lewis will have the same number of rocks.
Part C: To find out how many rocks Samuel and Lewis will have when the amount of rocks in their collection is equal, we substitute the value of 'w' into either equation. Let's use Samuel's equation:
S = 18 + 4w
S = 18 + 4(12)
S = 18 + 48
S = 66
Therefore, when Samuel and Lewis have the same number of rocks, they will both have 66 rocks in their collections.