Question

Students in a cooking class made 4 1/2 quarts of soup. They served 4/5 of the soup to friends. Each serving is 3/5 quart. Hector incorrectly says that there were 3 3/5 servings of soup. What is the correct number of servings? What did Hector do wrong?

Answer 1

The correct number of servings = 6.

By saying there were
`3(3)/(5)` servings of soup, Hector must have intended to say that there were
`3(3)/(5)` quarts of soup for serving.

Explanation:

Given:

Total quarts of soup made by students =
`4(1)/(2)`

Fraction of the soup served to friends =
`(4)/(5)`

Each serving =
`(3)/(5)` quarts

Hector incorrectly says that that there were
`3(3)/(5)` servings of soup.

To find the correct number of servings and to identify Hector's mistake.

Solution:

Total quarts of soup made =
`4(1)/(2)=(9)/(2)`

Fraction of total quarts served =
`(4)/(5)`

Thus, total quarts of soup served =
`(9)/(2)* (4)/(5)`

⇒
`(18)/(5)=3(3)/(5)`

Thus, total quarts of soup for serving =
`(18)/(5)` or
`3(3)/(5)`

Each serving =
`(3)/(5)` quarts

Total number of servings can be given as:

⇒
`(Total\ quarts\ of\ serving)/(Size\ of\ each\ serving)`

⇒
`((18)/(5))/((3)/(5))`

To divide fractions, we take reciprocal of the divisor and replace divsion with multiplication.

⇒
`(18)/(5)* (5)/(3)`

⇒
`(18)/(3)`

⇒ 6 servings

Thus, the correct number of servings = 6.

By saying there were
`3(3)/(5)` servings of soup, Hector must have intended to say that there were
`3(3)/(5)` quarts of soup for serving.