Question

On a fruit farm, 1/2 of the trees are apple trees and 1/4 are pear trees. The rest of the trees are peach trees. Out of the Apple trees, 2/3 of the trees have red apples and the rest have green apples. There are 60 trees in all. Select the boxes in the table to show whether each statement is true or false. Statement 1: 1/6 of the trees on the farm have green apples. Statement 2:There are 25 pear trees. Statement 3: There are 15 peach trees.

Answer 1

Statement 1: 1/6 of the trees on the farm have green apples. TRUE

Statement 2:There are 25 pear trees. FALSE

Statement 3: There are 15 peach trees. TRUE

Explanation:

Total number of trees = 60

Number of apple trees = 1/2

⇒Apple trees =
`(1)/(2)  * 60 = 30`

Number of pear trees = 1/4

⇒Apple trees =
`(1)/(4)  * 60 = 15`

So, the remaining trees = 60 - ( Number of apple + pear) trees

= 60 - ( 30 + 15) = 60 - 45= 15

⇒Number of peach trees = 15

Now, total apple trees = 30

So, number of red apple trees =
`(2)/(3)  *30 = 20`

⇒The number of green apple trees = Total apple trees - Red apple tress

= 30 - 20 = 10

Given statements are:

Statement 1: 1/6 of the trees on the farm have green apples.

1/6 of total farm =
`(1)/(6)  *60 = 10`

TRUE,as the number of green apple trees = 10.

Statement 2:There are 25 pear trees.

FALSE, as number of pear tress = 15

Statement 3: There are 15 peach trees.

TRUE