Sandy’s orchard has only apple trees and pear trees and she is wanting to add some avocado trees currently there are 4 apples trees for every 3 pear trees she is wanting to plant enough avocado trees so that’s she has 2 avocado trees for every 5 pears in the orchard.

Question

Sandy is planting 18 avocado trees making the ratio of avocado trees to apple trees _ to _

Answer 1

To find the ratio of avocado trees to apple trees, we need to determine the number of apple trees Sandy currently has.

Since there are 4 apple trees for every 3 pear trees, we can set up the equation:
(apple trees)/(pear trees) = 4/3

We know that there are 18 avocado trees, so there will be a total of (18 + apple trees) in the orchard.

We also know that Sandy wants the ratio of avocado trees to pear trees to be 2/5. So we can set up another equation:
(avocado trees)/(pear trees) = 2/5

Now we can set up a proportion to solve for the number of apple trees:
(18 + apple trees)/x = 2/5

Cross multiplying and solving for x, we get:
5(18 + apple trees) = 2x
90 + 5(apple trees) = 2x
5(apple trees) = 2x - 90
apple trees = (2x - 90)/5

Now, substituting this into the first equation, we get:
(2x - 90)/(3x - 90) = 4/3

Cross multiplying and solving for x, we get:
3(2x - 90) = 4(3x - 90)
6x - 270 = 12x - 360
6x - 12x = -360 + 270
-6x = -90
x = 15

Therefore, Sandy currently has 15 apple trees.

To find the ratio of avocado trees to apple trees, we substitute x = 15 back into (2x - 90)/5:
(2(15) - 90)/5 = 30/5 = 6/1

So the ratio of avocado trees to apple trees is 6 to 1.