Question

a recipe for a batch of 3 dozen chocolate chip cookies calls for 3 1/2 cups of flour, 1 cup of sugar, and 2 3/4 cups of chocolate chips. How much of each ingredient should be used to make 2 dozen cookies?

Answer 1

3 doz = 36 cookies, 2 doz = 24 cookies

36/3.5 = 24/x
36x = 84
x = 84/36
x = 2.33 = 2 1/3.......so for 2 doz, u need 2 1/3 cups flour

36/1 = 24/x
36x = 24
x = 24/36
x = .666 = 3/5...and 3/5 cup of sugar

36/2.75 = 24/x
36x = 66
x = 66/36
x = 1.83 cups of chocolate chips

Answer 2

Explanation:

A recipe for a batch of 3 dozen chocolate chip cookies calls for
`3(1)/(2)` cups of flour, 1 cup of sugar and
`2(3)/(4)` cups of chocolate chips.

We will calculate for each ingredients by unitary method.

∵ flour used in 3 dozen cookies =
`3(1)/(2)` or
`(7)/(2)` cups

∴ flour used in 1 dozen cookies =
`(7/2)/(3)` cups

∴ flour used in 2 dozen cookies =
`(7/2)/(3)` × 2

=
`(7)/(6)` × 2

=
`(14)/(6)`

=
`(7)/(3)`

=
`2(1)/(3)` cups

∵ sugar is used in 3 dozen cookies = 1 cup

∴ sugar is used in 1 dozen cookies =
`(1)/(3)`

∴ sugar is used in 2 dozen cookies =
`(1)/(3)` × 2

=
`(2)/(3)` cups

∵ chocolate chips are used in 3 dozen cookies =
`2(3)/(4)` =
`(11)/(4)` cups

∴ in 1 dozen cookies chocolate chips used =
`(11/4)/(3)`

∴ in 2 dozen cookies chocolate chips used =
`(11/4)/(3)` × 2

=
`(11)/(12)` × 2

=
`(11)/(6)`

=
`1(5)/(6)` cups

To make 2 dozen cookies each ingredient should be used :

`2(1)/(3)` cups of flour

`(2)/(3)` cups of sugar

`1(5)/(6)` cups of chocolate chips