Question

A cook makes vegetable barley soup by mixing 2 pounds of barley into 7 2 quarts of vegetable broth. How many pounds of barley should the cook mix with 21 quarts of broth?

a. The cook should mix 6 pounds of barley.
b. The cook should mix 8 pounds of barley.
c. The cook should mix 12 pounds of barley.
d. The cook should mix 14 pounds of barley.

Answer 1

Using a proportion based on the initial recipe, we find that the cook should mix 6 pounds of barley with 21 quarts of broth.

Step-by-step explanation:

The question involves setting up a proportion to determine how much barley to use for a larger amount of broth, based on the ratio given in the initial scenario. We know from the initial recipe that 2 pounds of barley are used for 72/4 quarts of vegetable broth, which simplifies to 2 pounds of barley for every 2 quarts of vegetable broth after dividing 72/4 by the conversion factor that 1 quart = 2 pints.

To find the amount of barley needed for 21 quarts of broth, we set up the proportion as follows:

(2 pounds of barley) / (2 quarts of broth) = (x pounds of barley) / (21 quarts of broth)

Solving for x gives us:

x = (2 pounds of barley) * (21 quarts of broth) / (2 quarts of broth)

x = 21 pounds of barley

Thus, the cook should mix 6 pounds of barley with 21 quarts of broth.