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?
A.y=75x+20

B.y=20x+75

C.y=75x−20

D.y=20x−75


To solve this problem, we need to find the equation that represents the total number of coins George has after \( x \) months. Here's the breakdown:

1. **Starting Amount**: George starts with 75 coins. This is a constant value.

2. **Monthly Addition**: He adds 20 coins every month, so the total number of coins increases by 20 for each month.

The general form for a linear equation is:
\[
y = mx + b
\]
Where:
- \( y \) is the total number of coins after \( x \) months.
- \( m \) is the rate of change (number of coins added each month).
- \( x \) is the number of months.
- \( b \) is the starting amount (initial number of coins).

Substituting the given values:
- The starting amount \( b \) is 75.
- The rate of change \( m \) is 20.

Thus, the equation becomes:
\[
y = 20x + 75
\]

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

Would you like more details or have any questions?

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### Related Questions:
1. How would the equation change if George added 30 coins each month instead of 20?
2. What would the equation look like if George started with 100 coins?
3. How many coins will George have after 5 months?
4. If George decided to add a different number of coins each month, how could we represent this situation with a non-linear equation?
5. How can we graph the equation \( y = 20x + 75 \) to visualize George's coin collection growth over time?

### Tip:
In word problems, always identify the starting value and the rate of change to set up the correct linear equation.

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 represent George's growing coin collection. Starting with 75 coins and adding 20 coins each month, this problem teaches linear growth using the equation y = 20x + 75. Ideal for students in Grades 6-8 learning algebra and linear equations.

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