Question

Anne's recipe to make `2` dozen cookies calls for `3/4` cup of sugar. How much sugar will she need if she is to bake `4 1/2`dozen cookies?

Answer 1

2 dozen cookies is 24 cookies

Find out how much sugar is needed for 1 cookie

`(3/4)/24`

24 can be written as a fraction `24/1` so

`(3/4)/(24/1) =` sugar per cookie

Multiply both the top (numerator) and bottom denominator by 1/24
This is math magic, it makes the bottom disappear.

`24/1 xx 1/24 = 1` leaving

`3/4 xx 1/24 = cancel3/(4 xx cancel3 xx 8)` ( breaking 24 into 3 x 8 )

`1/ 4 xx 8 = 1/32`

so `1` cookie takes `1/32` cups of sugar.

`4 1/2` dozen cookies equals `54` cookies so

`54 xx 1/32` = the number of cups of sugar.

`54 xx 1/32 = 54/32 = 1 22/32 = 1 11/16`

so it will take `1 11/16` cups of sugar to make `4 1/2` dozen cookies.

Answer 2

`1 11/16` cups of sugar are needed.

[This is just less than `1 3/4` cups.]

Explanation:

This is an example of direct proportion. The more cookies that are baked, the more sugar will be needed.

Write the proportion as an equivalent fraction:

`2` dozen cookies needs `3/4` cup sugar.
`4 1/2` dozen cookies needs `x` cups sugar.

`2/(3/4) = (4 1/2)/x" "larr` cross multiply

`2x = 3/4 xx 4 1/2" "larr` simplify

`2x = 3/4 xx 9/2 = 27/8`

`x = 27/8 xx 1/2`

`x = 27/16`

`x = 1 11/16` cups of sugar