Question

José is making fruit-filled tart shells for a party. He has 72 raspberries and 108 blueberries. He wants the same number of each type of fruit in each tart. If he puts the greatest possible number of fruits in each tart, how many tarts can he make?

Answer 1

If he puts the greatest possible number of fruits in each tart, José can make 5 tarts?

Answer 2

It's not clear just what you mean by "the greatest number" If you put 72 of each berry into each tart, you can make only 1.

If you put 36 of each kind of berry into each tart, then you can make only 2 tarts, with 36 blueberries left over.

If you put 3 raspberries and 4 blueberries in each tart, you can make exactly 24 tarts.

If you put 8 raspberries and 12 blueberries in each tart, you can make exactly 9 tarts.

Since there are 2/3 as many raspberries as blueberries, to use up all the berries, you will need 2/3 as many in each tart.

Answer 3

The GCF for both 72 and 108 is 36. So 36 berries will be in each tart.