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To determine the correct equation for the total number of coins, \( y \), in George's collection after \( x \) months, let’s analyze the information given:

1. **Initial number of coins:** George starts with 75 coins.
2. **Monthly addition:** Each month, he adds 20 coins to his collection.

The total number of coins \( y \) after \( x \) months can be represented by an equation that starts with the initial amount and adds 20 coins for each month.

The equation is:
\[
y = 75 + 20x
\]

Let's check the answer choices to find the matching equation:
- **Option A:** \( y = 75x + 20 \) - This would mean he starts with 20 coins and adds 75 each month, which is incorrect.
- **Option B:** \( y = 20x + 75 \) - This is correct because it starts with 75 coins and adds 20 coins each month.
- **Option C:** \( y = 75x - 20 \) - This would mean a decrease in coins each month, which is incorrect.
- **Option D:** \( y = 20x - 75 \) - This also incorrectly implies a negative initial amount.

The correct answer is **B. \( y = 20x + 75 \)**.

Would you like a further breakdown of this solution?

Here are some related questions to deepen understanding:
1. How would the equation change if George added 25 coins each month instead?
2. What would the equation look like if he started with 100 coins instead?
3. How would you solve for \( x \) if you knew the total number of coins \( y \)?
4. What if he started with 75 coins but gave away 5 coins each month?
5. How would the answer change if George’s dad gave him a different number of coins to start?

**Tip:** When setting up a linear equation for a situation like this, think of the initial amount as the intercept (starting point) and the monthly change as the slope (rate of increase).

George started a coin collection. His dad gave him 75 coins. Each month he will add 20 coins to the collection. Which equation can be used to find y, the total number of coins in George's collection after x months?

Find the correct linear equation to determine the total number of coins in George's collection after x months. The problem starts with 75 initial coins and adds 20 coins per month. Suitable for students in Grades 6-8.

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