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There were 104 cookies in a box. The number of raisin cookies was 6/7 the number of plain cookies. Trisha ate an equal number of raisin and plain cookies. As a result, the ratio of the number of raisin cookies to the number of plain cookies left was 3:5. How many raisin cookies were left in the end?

 Apr 18, 2021
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Hi! 

 

If we say that x is the number of plain cookies, then 6x/7 is the number of raisin cookies. If we add x and 6x/7, we get 13x/7.

 

13x/7 = 104 

13x = 728

x = 56

 

We have 56 plain cookies and 48 raisin cookies. Now we need to take a certain number away from both of these numbers to get a ratio of 3:5. 

 

(48-  x)/(56 - x) = 3 / 5

(48-  x)5 = (56 - x)3

240 - 5x = 168 - 3x

72 = 2x

36 = x

 

Now that we have this number, we can find out that there are 48 - 36 = 12 raisin cookies left.

 Apr 18, 2021

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