Question

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? a. 4 b. joanie doesnt have any gray shirts. c. 2 d. 1

Explanation:

Step1: Define variables

Let the number of gray shirts be $g$, black shirts be $b$, white shirts be $w$.
We know that $w = 5g$, $b=3g + 3$, and after donating 1 white - shirt, the number of black and white shirts is the same, so $w - 1=b$.

Step2: Substitute the expressions for $w$ and $b$

Substitute $w = 5g$ and $b = 3g+3$ into $w - 1=b$.
We get $5g-1=3g + 3$.

Step3: Solve the equation for $g$

Subtract $3g$ from both sides: $5g-3g-1=3g-3g + 3$, which simplifies to $2g-1=3$.
Add 1 to both sides: $2g-1 + 1=3 + 1$, so $2g=4$.
Divide both sides by 2: $g = 2$.

Answer:

C. 2