How much grape juice would you need to mix with 15/4 quarts of sparkling water. (a recipe for sparkling grape juice calls for 1 1/2 quarts of sparkling water and 3/4 quart of grape juice)

15/8 quarts

Step-by-step explanation:

The recipe calls for 1 1/2 quarts of sparkling water.  This can be written as the improper fraction 3/2 (this is because 1 whole = 2/2; 2/2 + 1/2 = 3/2).

Using 15/4 quarts sparkling water means we used 5/2 times as much as the recipe calls for.  This means we would use 5/2 times the amount of grape juice as well; 5/2(3/4) = 15/8.

hello from mrbilldoesmath!

answer:

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

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

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

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb