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?
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
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