MHB (Fractions) How many cookies did Meiling bake

[Johnx1]

Meiling baked some cookies. 5/7 of the cookies were butter cookies and the rest were green tea cookies. She gave away 3/4 of the butter cookies and 1/4 of the green tea cookies. After she ate 9 green tea cookies, she had an equal number of butter cookies and green tea cookies left. How many cookies did Meiling bake?

My work:

Number of butter cookies = B
Number of Green Tea cookies = G
Number of total cookies = T (not sure about this one)

We know there are 2/7G of the total cookies because 5/7B

Then I did 3/4B = 1/4G - 9.

I tried different ways, but I couldn't find a correct way to do it.

 

[skeeter]

Meiling baked some cookies. 5/7 of the cookies were butter cookies and the rest were green tea cookies. She gave away 3/4 of the butter cookies and 1/4 of the green tea cookies. After she ate 9 green tea cookies, she had an equal number of butter cookies and green tea cookies left. How many cookies did Meiling bake?

My work:

Number of butter cookies = B
Number of Green Tea cookies = G
Number of total cookies = T (not sure about this one)

We know there are 2/7G of the total cookies because 5/7B

Then I did 3/4B = 1/4G - 9.

I tried different ways, but I couldn't find a correct way to do it.

let x = total number of cookies

number of butter cookies = 5x/7

number of tea cookies = 2x/7

number of butter cookies left = (1/4)(5x/7) = 5x/28

number of tea cookies left = (3/4)(2x/7) - 9 = 3x/14 - 9

5x/28 = 3x/14 - 9

5x = 6x - 252

x = 252

check ...

B = (5/7)252 = 180

T = (2/7)252 = 72

gave away (3/4)180 = 135 ... number of butter cookies left = 45

gave away (1/4)72 + ate 9 = 27 ... number of tea cookies left = 45

 

[Johnx1]

number of butter cookies left = (1/4)(5x/7) = 5x/28

number of tea cookies left = (3/4)(2x/7) - 9 = 3x/14 - 9

I see where I made the mistake. I had to times the number of cookies that were left.

Thank you.