https://file.aiquickdraw.com/mathbot/file/17278116455277ore709f.jpg

Let's analyze the problem step by step, based on the information and equation provided.

### The equation:
\[ y - 10 = -2(x - 10) \]
This equation models the amount of money Hugo still needs to pay for the bicycle, where:
- $ x $ is the number of weeks.
- $ y $ is the amount of money left to pay.

We can rewrite this equation in a simpler form by solving for $ y $:

### Simplifying the equation:
1. Distribute the $-2$ on the right-hand side:
   \[ y - 10 = -2x + 20 \]
   
2. Add 10 to both sides to isolate $ y $:
   \[ y = -2x + 30 \]

This is the linear equation that shows the relationship between the number of weeks $ x $ and the money left to pay $ y $.

### Part 1: How much did the bicycle cost?
At $ x = 0 $ (the starting point, or when Hugo hasn't paid anything yet), the total cost of the bicycle is equal to $ y $.

Substitute $ x = 0 $ into the equation:
\[
y = -2(0) + 30 = 30
\]
So, the bicycle cost **$30**.

### Part 2: After how many weeks will Hugo finish paying for the bike?
Hugo finishes paying when $ y = 0 $ (no money left to pay). Let's solve for $ x $ when $ y = 0 $:

\[
0 = -2x + 30
\]
Solve for $ x $:
\[
2x = 30 \quad \Rightarrow \quad x = 15
\]

Therefore, Hugo will finish paying for the bike after **15 weeks**.

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Would you like more details on any specific part of the solution? 

Here are 5 related questions to consider:

1. How does the slope $-2$ of the line help understand Hugo's payments?
2. What does the $y$-intercept (30) represent in this context?
3. How would the graph of the equation look with the points plotted?
4. How can we use the table of values to double-check the solution?
5. What would change if Hugo increased his weekly payments?

### Tip:
In linear models, the slope indicates the rate of change, and in this case, it's how fast Hugo is reducing his debt over time.

Hugo decided to pay $2 a week to his brother to buy a bicycle. The equation y − 10 = −2(x − 10) models the amount of money he owes for the bike, where x is the number of weeks and y is the amount of money he still needs to pay. How much did the bicycle cost? After how many weeks will Hugo finish paying for the bike?

Learn how to solve Hugo's bicycle payment problem using a linear equation. This detailed solution explains how to find the total cost of the bike and the number of weeks it will take to finish payments. The problem is modeled using y = -2x + 30 and is suitable for Grades 7-8.

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