Answer:
Let's define:
P = pies that Phoebe ate
F = pies that Finn ate
We know that together they ate 29/12 pies, then:
P + F = 29/12
We know that Finn ate more than Phoebe, then F > P.
And we know that Phoebe ate more than 5/6 of a pie, then:
P > 5/6.
Then we have the relations:
P + F = 29/12
P > 5/6
F > P
To find different combinations we can just give one of the variables a value.
We have a direct condition on P, which is:
P > 5/6
So we can just give P any value larger than 5/6 and find the value of F.
For example:
P = 6/6 = 1
Then:
F + 1 = 29/12
F = 29/12 - 1 = 29/12 - 12/12 = 17/12
And 17/12 > 5/6
So we meet the condition F > P.
Then we have the combination:
P = 1
F = 17/12
Now let's find another condition, this time let's use:
P = 5/6 + 1/12 = 10/12 + 1/12 = 11/12
Then:
F + 11/12 = 29/12
F = 29/12 - 11/12 = 18/12
And 18/12 > 11/12
Then we meet the condition:
F > P.
We have the combination:
F = 18/12
P = 11/12
Now for the last combination, we can use:
P = 5/6 + 3/12 = 10/12 + 3/12 = 13/12
Then:
F + 13/12 = 29/12
F = 29/12 - 13/12
F = 16/12
And 16/12 > 13/12
Then we meet the condition F > P
We have the combination:
F = 16/12
P = 13/12.
