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. 2
b. 1
c. 4

Option A. 2

Step-by-step explanation:

To solve this problem we can write equations for each shirt color.

Let's call:

b = black shirts

g = gray shirts

w = white shirts

B = brown shirts

If you have 3 times more black shirts than gray shirts and buy 3 more black shirts then:

    (i)

If you have 5 times more white shirts than gray shirts and gave a white shirt then:

     (ii)

It has 2 times more gray shirts than brown camsas, then:

        (iii)

It has the same amount of black and white shirts

           (iv)

We want to find the number of gray shirts.

Then replace (iv) in (ii)

       (v)

Now substitute (v) into (i) and clear g.

Joan has 2 gray shirts

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1