Question

Phoebe and finn are sharing

some pies together, they have
eaten 29/12 of the pies fin ate
mor e pie than phoebe.phoebe
ate mor than 5/6 of a pie what
fraction of pie could phoebe and
finn each have eaten? show 3
combinations

Answer 1

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.