Joanie is organizing her closet. She has 3 times as many black shirts as gray shirt, plus 3 new black shirts she bought. She has 5 times as many white shirts as gray shirts. If she has the same number of black and white shirts, how many grey shirts does Joanie have.

Question

Joanie is organizing her closet. She has 3 times as many black shirts as gray shirt, plus 3 new black shirts she bought. She has 5 times as many white shirts as gray shirts. If she has the same number of black and white shirts, how many grey shirts does Joanie have.

Answer 1

Let g be the number of gray shirts.

Joanie has 3g + 3 black shirts.
She also has 5g white shirts.
She has 3g + 3 = 5g black shirts.
Substituting the second equation into the third equation, we get 3g + 3 = 5g.
Subtracting 3g from both sides, we get 3 = 2g.
Dividing both sides by 2, we get g = 3. Answer: \boxed{3}.

Answer 2

Joanie is organizing her closet. She has 3 times as many black shirts as gray shirt, plus 3 new black shirts she 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 grey shirts does Joanie have?

Answer 3

Let's call the number of gray shirts "g".

Since Joanie has 3 times as many black shirts as gray shirts, she has 3g black shirts, plus 3 new ones, giving her a total of 3g + 3 black shirts.
She has 5 times as many white shirts as gray shirts, minus the 1 she donated, giving her 5g - 1 white shirts.
If she has the same number of black and white shirts, that means 3g + 3 = 5g - 1.
By adding 1 to both sides of the equation, we get 3g + 4 = 5g.
By subtracting 3g from both sides of the equation, we get 4 = 2g.
Now we can divide both sides of the equation by 2, giving us g = 2.
So Joanie has \boxed{2} gray shirts.

Answer 4

To find out how many gray shirts Joanie has, let's set up an equation:

Let's say the number of gray shirts is "x."

According to the given information, Joanie has 3 times as many black shirts as gray shirts, which means she has 3x black shirts. Additionally, she bought 3 new black shirts, so she now has 3x + 3 black shirts.

Joanie also has 5 times as many white shirts as gray shirts, which means she has 5x white shirts.

Since Joanie has the same number of black and white shirts, we can set up the following equation:

3x + 3 = 5x

Now, we can solve this equation to find the value of x, which represents the number of gray shirts Joanie has:

Subtract 3x from both sides: 3 = 2x

Divide both sides by 2: x = 3/2 = 1.5

Since we can't have partial gray shirts, we can conclude that Joanie has 1 gray shirt.