Question

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.

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.

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.

Answer 1

Part A: Y=4x+18 Y=3x+30
Part b: y-4x=18 y-3x=30 then you do substitution -(y-4x=18) y-3x=30
Then distribute -y+4x=-18 y-3x=30
Then add x=12
Then plug in 12 for x y=66
So the answer is 12 weeks
Part c: the answer is 66 rocks because we plugged 12 into the equation