Twenty percent of the trees in an orchard are apple trees, and 1/3 of the trees that are not apple trees are cherry trees. if 3/4 of the trees in the orchard are fruit trees, and the only types of fruit trees in the orchard are apple, cherry, and plum, what fraction of the trees in the orchard are plum trees?

The required fraction is 17/60

Step-by-step explanation:

Consider the provided information.

Let us assume that the number number if trees are 60.

It is given that 20% are apple tree.

Therefore, 12 trees are apple tree.

That means non apple trees are:

Non apple trees = 60 - 12 = 48

It is given that and 1/3 of the trees that are not apple trees are cherry trees.

Cherry trees = 1/3 × 48 = 16

The cherry trees are 16.

3/4 of the trees in the orchard are fruit trees,

Fruit trees = 3/4 × 60 = 45

Total fruit tree are 45

Plum trees = 45 - 12 - 16 = 17

Hence, the number of plum trees are 17

We need to find fraction of the trees in the orchard are plum trees

Fraction = 17/60

Hence, the required fraction is 17/60

60: 45 =12: 9 =4: 3 so the answer is 4: 3