Afarm stand sells apples pies and jars of applesauce. the table shows the number of apples needed to make a pie and a jar of applesauce. yesterday, the farm picked 321 granny smith apples and 173 golden delicious apples. how many pies and jars of applesauce can the farm make if every apple is used? type of apple granny smith golden delicious needed for a pie 9 5 needed for a jar of applesauce 8 4 the farm can make pies and jars of applesauce.

ratio is 2 : 9

the answer is three

13.5 : 3

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)