Masha had 20p scoops of ice cream and liz had 180 scoops of ice cream. after they each ate an equal number of scoops, the ratio of the number of scoops that masha had remaining to number of scoops liz had remaining was 3: 2. how many scoops did they each eat?

  140 scoops

Step-by-step explanation:

Assuming Masha started with 200 scoops of ice cream, each ate 140 scoops.

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The difference in ratio units is 3-2 = 1.

The difference in ice cream scoops is 200 -180 = 20, so each ratio unit must stand for 20 scoops of ice cream. That is, Masha and Liz ended with 3·20 = 60 and 2·20 = 40 scoops of ice cream remaining, respectively.

In order to have these numbers remaining, each had to eat ...

  200 -60 = 180 -40 = 140 scoops of ice cream

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18