Joanie is organizing her closet. She has 3 times as many black shirts as gray shirts, plus 3 new black shirts she just bought. She has 5 times as many white shirts as gray shirts, minus the 1 white shirt she donated. Joanie has 2 times more gray shirts than brown shirts. If she has the same number of black and white shirts, how many gray shirts does Joanie have?

Let the number of gray shirts be denoted by \( g \), and the number of brown shirts by \( b \).

### Step 1: Express black shirts in terms of gray shirts
Joanie has 3 times as many black shirts as gray shirts, plus 3 new black shirts she just bought. So, the total number of black shirts is:
\[
B = 3g + 3
\]

### Step 2: Express white shirts in terms of gray shirts
Joanie has 5 times as many white shirts as gray shirts, minus 1 white shirt she donated. So, the total number of white shirts is:
\[
W = 5g - 1
\]

### Step 3: Relate gray shirts and brown shirts
Joanie has 2 times more gray shirts than brown shirts, meaning the number of gray shirts is 2 more than twice the number of brown shirts:
\[
g = 2b + 2
\]

### Step 4: Use the fact that black shirts equal white shirts
The problem states that Joanie has the same number of black and white shirts. Thus, we set \( B = W \):
\[
3g + 3 = 5g - 1
\]

### Step 5: Solve for \( g \)
Simplify the equation:
\[
3g + 3 = 5g - 1
\]
Subtract \( 3g \) from both sides:
\[
3 = 2g - 1
\]
Add 1 to both sides:
\[
4 = 2g
\]
Divide by 2:
\[
g = 2
\]

### Step 6: Conclusion
Joanie has \( \boxed{2} \) gray shirts.

Would you like more details on any step, or do you have further questions?

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Here are 5 related questions:
1. How many black shirts does Joanie have?
2. How many white shirts does Joanie have?
3. How many brown shirts does Joanie have?
4. What if Joanie had donated 2 white shirts instead of 1?
5. What would happen if Joanie bought 5 new black shirts instead of 3?

**Tip:** When solving word problems, organizing known information into algebraic expressions is key to avoiding confusion!

Discover how to solve a linear equation word problem involving black, white, gray, and brown shirts. Joanie has a closet full of shirts with different ratios between colors. Learn how algebra helps us find the number of gray shirts Joanie has, based on key data points. Ideal for Grades 6-8.

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