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The ratio of Keith's marshmallows to Pico's marshmallows was 7:6. After Keith ate 44 marshmallows, the ratio became 1:2. How many fewer marshmallows did Keith have than Pico then?

 Apr 15, 2021
 #1
avatar+31412 
+1

keith has  7 /13 of the total

 

(7/13x )  - 44  =  1/3(x -44)

21/39 x - 44 = 13/39 x - 44/3

    8/39 x  = 44 - 44/3 

 

 x = 143      Kieth had 77   Pico had 66    then keith ate 44 leaving him 33       and  33 less than Pico

 Apr 15, 2021
 #2
avatar+118586 
+1

Call  the  number  of  marshmalows  the  Keith started  with =  N

Then  Pico's  number  was  (6/7) N

 

After  Keith  eats  44, we  have  that

 

(N - 44)              1

______  =        ___            cross-multiply

  (6/7)N              2

 

2 ( N -44)  =  (6/7)N

 

2N  - 88  = (6/7)N

 

2N - (6/7)N  =   88

 

(14/7)N  - (6/7)N  =  88

 

(8/7)N  =  88

 

N =  88 (  7/8)   =    77  =  what Keith  started with

 

(6/7)N   = (6/7) (77)  =  66  =  what Pico started with

 

After Keith  atee  44  he had  33 left  

 

So  he  had  33 fewer  marshmallows  than Pico

 

cool cool cool

 Apr 15, 2021

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