Let the original number of marbles in each bag be $x$.

Step 1: Express the changes to the number of marbles

• Jimmy's marbles:

  • Jimmy originally had $x$ marbles.
  • He gained 5 marbles, so he now has $x + 5$ marbles.

• Jake's marbles:

  • Jake originally had $x$ marbles.
  • He ended up with double his original amount minus 3 marbles, so he now has $2x - 3$ marbles.

Step 2: Set up the equation

We know that by the end of lunch, they had the same number of marbles: $x + 5 = 2x - 3$

Step 3: Solve the equation

1. Subtract $x$ from both sides: $5 = x - 3$
2. Add 3 to both sides: $x = 8$

Final Answer:

Originally, there were 8 marbles in each bag.

Would you like details or have any questions?

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Here are five related questions to explore further:

1. If Jimmy had lost 5 marbles instead of gaining them, how many marbles would he and Jake have had at the end?
2. What would happen if Jake had ended up with triple his original number of marbles minus 2 instead?
3. If they started with different amounts of marbles, how would that change the solution?
4. What if both Jimmy and Jake each had to give away 4 marbles during lunch? How many would they have had at the end?
5. How many marbles would they have each started with if Jake had ended up with 5 more than twice his original amount?

Tip: When solving word problems involving changes to quantities, carefully translate the words into algebraic expressions to set up the correct equations.