MHB (Fractions) How many cookies did Meiling bake

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Meiling baked a total of 252 cookies, with 180 being butter cookies and 72 green tea cookies. She gave away 135 butter cookies (3/4 of the total) and 27 green tea cookies (1/4 of the total) before eating 9 green tea cookies. After these actions, she had an equal number of 45 butter cookies and 45 green tea cookies left. The calculations confirmed that the distribution and remaining cookies matched the conditions given in the problem. The final answer to how many cookies Meiling baked is 252.
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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.
 
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Johnx said:
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
 
skeeter said:
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.
 

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