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)
Sam = 18 + 4w
Lew = 30 + 3w
we want Sam = Lew
18 + 4w = 30 + 3w
4w - 3w = 30 - 18
w = 12
after 12 weeks they have the same
since their total should be equal...
Sam = 18 + 4w = 18 + 48 = 66 rocks
(we get the same if we evaluate Lew)
Part A:
Let S be the number of weeks and R be the number of rocks in their collections.
For Samuel:
R(Samuel) = 18 + 4S
For Lewis:
R(Lewis) = 30 + 3S
Part B:
To find out after how many weeks Samuel and Lewis will have the same number of rocks in their collections, we need to set the two equations equal to each other and solve for S.
18 + 4S = 30 + 3S
Subtracting 3S from both sides:
18 + S = 30
Subtracting 18 from both sides:
S = 12
Therefore, after 12 weeks, Samuel and Lewis will have the same number of rocks in their collections.
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 S (which we found in Part B) into either equation.
Using the equation for Samuel:
R(Samuel) = 18 + 4S
R(Samuel) = 18 + 4(12)
R(Samuel) = 18 + 48
R(Samuel) = 66
Therefore, both Samuel and Lewis will have 66 rocks when the amount of rocks in their collections is equal.
Part A:
Let S represent the number of weeks since Samuel started collecting rocks and L represent the number of weeks since Lewis started collecting rocks.
The equation for Samuel's collection is:
S = 18 + 4S
The equation for Lewis' collection is:
L = 30 + 3L
Part B:
To find the number of weeks when Samuel and Lewis have the same number of rocks, we need to set the two equations equal to each other and solve for the number of weeks, which is represented by S and L:
18 + 4S = 30 + 3L
Simplifying the equation:
4S - 3L = 12
Part C:
To find out how many rocks Samuel and Lewis will have when the amount in their collections is equal, we need to substitute the value of S or L back into either of the original equations.
Let's solve for S:
4S = 12 + 3L
S = (12 + 3L) / 4
We can substitute this value back into Samuel's equation to find the number of rocks:
Samuel's collection = 18 + 4S
Samuel's collection = 18 + 4[(12 + 3L) / 4]
Simplifying the equation:
Samuel's collection = 18 + 12 + 3L
Samuel's collection = 30 + 3L
Similarly, we can substitute L back into Lewis' equation to find the number of rocks:
Lewis' collection = 30 + 3L
When the number of rocks in their collections is equal, Samuel and Lewis will have 30 + 3L rocks each.