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# Challenging Ratios

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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
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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
+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   Apr 15, 2021