(Fractions) How many cookies did Meiling bake

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In summary, Meiling baked some 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.
  • #1
Johnx1
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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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  • #2
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
 
  • #3
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.
 

1. How do you calculate fractions?

In order to calculate fractions, you need to divide the top number (numerator) by the bottom number (denominator). For example, if Meiling baked 3/4 of a batch of cookies, you would divide the total number of cookies by 4 and then multiply by 3 to get the number of cookies Meiling baked.

2. What is the difference between a proper and improper fraction?

A proper fraction is one where the numerator is smaller than the denominator, for example 1/2. An improper fraction is one where the numerator is equal to or larger than the denominator, for example 5/4.

3. How can I simplify fractions?

To simplify fractions, you need to find the greatest common factor (GCF) of the numerator and denominator. Then, divide both numbers by the GCF to get the simplified fraction. For example, if Meiling baked 12/24 of a batch of cookies, the GCF is 12 and the simplified fraction would be 1/2.

4. What is the relationship between fractions and decimals?

Fractions and decimals are two different ways of representing the same value. Fractions use a numerator and denominator, while decimals use a decimal point and digits after the decimal point. You can convert between fractions and decimals by dividing the numerator by the denominator.

5. How many cookies did Meiling bake if she used 1/3 of the batch of cookie dough?

If Meiling used 1/3 of the batch of cookie dough, she baked 1/3 of the total number of cookies. To find the number of cookies she baked, you would multiply the total number of cookies by 1/3. For example, if there were 36 cookies in the batch, Meiling would have baked 12 cookies (36 x 1/3 = 12).

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