Achef is going to use a mixture of two brands of italian dressing. the first brand contains 9% vinegar, and the second brand contains 14% vinegar. the chef wants to make 310 milliliters of a dressing that is 13% vinegar. how much of each brand should she use?

Step-by-step explanation:

Let x represent the quantity in mL of the second brand of dressing (the one with the most vinegar). Then (310 -x) will be the quantity of the first brand of dressing. The total amount of vinegar in the mixture will be ...

  0.14x +0.09(310 -x) = 0.13·310

  0.05x + 0.09·310 = 0.13·310 . . . . . . . . . . eliminate parentheses

  0.05x = (0.13 -0.09)·310 = 0.04·310 . . . . subtract 0.09·310

  x = 4/5·310 = 248 . . . . divide by 0.05; the amount of second brand

  310-x = 62 . . . . . . . . . . the amount of first brand

The chef should use 62 mL of the first brand and 248 mL of the second brand.

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

the anwers is yes.