Question

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?

Answer 1

Answer:

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!!!