Question

Andy, Barry, and Craig are all in a pie-eating contest. Andy ate 4/7 of his pie, Barry ate 7/12 of his pie, and Craig ate 5/8 of his pie. Afterward, their dog Fido ate all the remaining pie. How many more pies did Fido eat than the winner? Express your answer as a fraction or mixed number in simplest form.

Answer 1

`(1)((142)/(168))` is the excess eaten by Fido.

Explanation:

The eaten pie ratios are as follows, Andy ate 4/7 of his pie, Barry ate 7/12 of his pie, and Craig ate 5/8 of his pie.

The winner of the contest is Craig, who ate (
`(5)/(8)`) of his pie, which is 62.5 %.

The remaining parts of pie are given by,

=
`(1-(4)/(7))+(1-(7)/(12))+(1-(5)/(8))`

=
`(3)/(7) + (5)/(12) + (3)/(8)`

=
`(205)/(168)`

This was the amount eaten by dog Fido.

The excess eaten by Fido than winner is,

=
`(205)/(168) - (5)/(8)`

=
`(310)/(168)`

=
`(1)((142)/(168))`