To solve the problem in the image, let's analyze the situation step by step.

Problem Summary:

• Luke initially had $111.
• After Jennifer spent $43, Luke had 3 times as much money as Jennifer.
• We need to find out how much more money Luke had than Jennifer at first.

Steps to Solve:

1. Let $J$ be the amount of money Jennifer had initially.

2. After Jennifer spent $43, she has $J - 43$ left.

3. According to the problem, Luke's money is 3 times Jennifer's remaining money: $111 = 3 \times (J - 43)$

4. Now, solve the equation for $J$: $111 = 3 \times (J - 43)$ Divide both sides by 3: $37 = J - 43$ Add 43 to both sides: $J = 80$

   So, Jennifer had $80 initially.

5. Determine how much more money Luke had than Jennifer initially: $111 - 80 = 31$ Therefore, Luke had $31 more than Jennifer at first.

Final Answer:

Luke had $31 more than Jennifer at first.

Would you like more details or have any questions?

Here are some related questions for further practice:

1. If Jennifer had $100 initially, how much did she have left after spending $43?
2. How much money did Luke have after Jennifer spent $43?
3. If Luke had 4 times as much money as Jennifer after her spending, what would Jennifer's initial amount be?
4. What if Jennifer spent $50 instead? How would that change the problem?
5. Can you create a similar problem but with different numbers and solve it?

Tip: When solving problems involving comparisons like "3 times as much," always set up the equation carefully to relate the amounts.