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

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step-by-step explanation:

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let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!