Question

Jeff is baking a cake. The recipe says that he has to mix 32 grams of vanilla powder to the flour. Jeff knows that 1 cup of that particular vanilla powder has a mass of 128 grams. He added two over three of a cup of vanilla powder to the flour. Should Jeff add more vanilla powder to make the exact recipe or did he go over and by what amount?

Answer 1

Jeff has add more vanilla powder to the exact recipe.

He had to start over again by only adding
`(1)/(4)` cups of vanilla to the flour.

Explanation:

1 cup of that particular vanilla powder has a mass of 128 grams

1 cup = 128 grams

Cups of vanilla added by Jeff =
`(2)/(3)`

Mass of
`(2)/(3)` cups of vanilla :

`(2)/(3)* 128 grams=(128)/(3) grams=85.33 grams`

Mass of vanilla required = 32 grams

Cups of vanilla required =
`(32)/(128) =(1)/(4) cup`

Jeff has already added 85.33 grams of vanilla which is greater the mass of 32 grams of vanilla. So, he had to start over again by only adding
`(1)/(4)` cups of vanilla to the flour.

Answer 2

The situation above described that Jeff added two - thirds of 128 to the flour. The numerical value of (2/3)(128) is 85.33 grams. The recipe says to add only 32 grams of vanilla powder. Hence, Jeff went over the prescribed amount.

To determine the excess amount, subtract 32 from 85.33 which has a numerical value of 53.33 grams.