Lucy has $15 pocket money saved up. Lucy gets another $2 each week.
Charlie has no money saved. Charlie gets $5 each week.
How many weeks will it be until Lucy and Charlie have the same amount of money, and what is the amount they will each have at that time?

Above is an example of a question on the topic of simultaneous equations and linear coordinate geometry. I want you to design more questions like this.

Here are five similar questions based on the topic of simultaneous equations and linear coordinate geometry:

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1. **Hannah and Jake Saving for a Bicycle:**
   Hannah has $20 saved up and earns $3 per week from her part-time job. Jake, on the other hand, has $5 saved up and earns $4 per week. After how many weeks will they have the same amount of money, and what will that amount be?

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2. **Ella and Noah's Marathon Training:**
   Ella runs 5 miles a week but has already accumulated 30 miles of training. Noah starts with no previous miles but runs 7 miles a week. How many weeks will it take for Ella and Noah to have run the same total number of miles, and how many miles will they have run at that point?

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3. **Ben and Ava's Book Collection:**
   Ben has a collection of 50 books, and he buys 2 new books each week. Ava starts with only 10 books but buys 4 new books each week. After how many weeks will Ben and Ava have the same number of books, and how many books will they each have?

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4. **Kevin and Mia's Charity Fundraising:**
   Kevin has raised $100 for charity and raises $6 per day. Mia hasn't raised any money yet but raises $10 per day. In how many days will they have raised the same amount of money, and how much will it be?

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5. **Zoe and Liam’s Plant Growth:**
   Zoe’s plant is already 8 cm tall and grows 2 cm per day. Liam’s plant starts at just 1 cm but grows 3 cm per day. In how many days will Zoe’s and Liam’s plants be the same height, and what will that height be?

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**Tip:** When solving problems like these, it helps to write an equation for each person or object, then set the two equations equal to each other to find the point where they intersect.

Would you like detailed solutions for any of these questions, or have any further questions?

Lucy has $15 pocket money saved up. Lucy gets another $2 each week. Charlie has no money saved. Charlie gets $5 each week. How many weeks will it be until Lucy and Charlie have the same amount of money, and what is the amount they will each have at that time?

Learn how to solve a simultaneous equations problem where Lucy and Charlie save money at different rates. This problem involves linear equations and finding when two lines intersect. Suitable for students in Grades 6-8.

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