Sandy's orchard has only apple trees and pear trees and she is wanting to add some avocado trees. currently, there are 4 apple trees for every 3 pear trees. she is wanting to plant enough avocado trees so that she has 2 avocado trees for every 5 pear trees in the orchard.. sandy is planting 18 avocado trees, making the ratio of avocado trees to apple trees be to

The ratio is 3:10.

Step-by-step explanation:

Sandy's orchard has only apple trees and pear trees.

There are 4 apple trees for every 3 pear trees.

She is wanting to plant enough avocado trees so that she has 2 avocado trees for every 5 pear trees in the orchard.

Sandy is planting 18 avocado trees, when we have 2 avocado trees for every 5 pear trees

Then we have 1 avocado trees for every 2.5 pear trees.

Therefore, if we have 18 avocado trees then we will have = 45 pear trees

Also, we have 4 apple trees for every 3 pear trees.

So, for 1 pear tree we have apple trees.

Lastly, if we have 45 avocado trees then we will have or rounding to 60 apple trees.

Hence, the ratio of avocado to apple trees = =

The ratio is 3:10.

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)