A cook used all of a two-pound chunk of cheese in making three recipes. Recipe I used one-third as much cheese as Recipe II did, and Recipe II used one-half as much cheese as Recipe III.

What part of the whole chunk of cheese, and how many pounds, did each recipe use?

Recipe I uses 10% of the whole chunk of cheese.

Recipe II uses 30% of the whole chunk of cheese.

Recipe II uses 60% of the whole chunk of cheese.

Recipe I uses 0.2 pounds of cheese.

Recipe II uses 0.6 pounds of cheese.

Recipe II uses 1.2 pounds of cheese.

Step-by-step explanation:

Total amount of cheese = 2 pounds

Recipe I used one-third as much cheese as Recipe II did, and Recipe II used one-half as much cheese as Recipe III.

Let the amount of cheese used by recipe I, II and III be x, y and z respectively.

Total amount of cheese = 2 pounds

x + y + z = 2 (eqn 1)

Recipe I used one-third as much cheese as Recipe II did

x = (1/3)y

y = 3x

Recipe II used one-half as much cheese as Recipe III.

y = (1/2)z

z = 2y

z = 2y = 2(3x) = 6x

Substituting all of these into eqn 1

x + y + z = 2

x + 3x + 6x = 2

10x = 2

x = 0.2 pounds of cheese

y = 3x = 0.6 pounds of cheese

z = 6x = 1.2 pounds of cheese.

Recipe I uses (0.2/2) = 10% of the whole chunk of cheese.

Recipe II uses (0.6/2) = 30% of the whole chunk of cheese.

Recipe II uses (1.2/2) = 60% of the whole chunk of cheese.

Hope this Helps!!!

3,750 deer

step-by-step explanation:

1,500 is 15 times larger than 100

lets make 250 15 times larger.

3750 deer

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