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. 2
B. 1
C. 4

Answer 1

Option A. 2

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:

`b = 3g +3` (i)

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

`w = 5g -1` (ii)

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

`g = 2B` (iii)

It has the same amount of black and white shirts

`b = w` (iv)

We want to find the number of gray shirts.

Then replace (iv) in (ii)

`b = 5g -1` (v)

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

`5g -1 = 3g +3\\\\5g -3g = 3 +1\\\\2g = 4\\\\g = 2`

Joan has 2 gray shirts