Question

Michael is baking cookies. His cookie recipe calls for 3/4 cups sugar and makes 24 cookies. If he wants to scale the recipe to make exactly 18 cookies, how many cups of sugar will he need? Express your answer as a mixed number.

Answer 1

9/16

Explanation:

24/6=4

18/6=3

(3/4)x(3/4)=9/16

Answer 2

`\begin{array}{ccll} \stackrel{cups}{sugar}&cookies\\ \cline{1-2} (3)/(4)&24\\[1em] x&18 \end{array}\implies \cfrac{ ~~ (3)/(4) ~~ }{x}~~ = ~~\cfrac{24}{18}\implies \cfrac{ ~~ (3)/(4) ~~ }{(x)/(1)}~~ = ~~\cfrac{4}{3}\implies \cfrac{3}{4}\cdot \cfrac{1}{x}=\cfrac{4}{3} \\\\\\ \cfrac{3}{4x}=\cfrac{4}{3}\implies 9=16x\implies \cfrac{9}{16}=x`

now, the fraction is not an improper one, thus we can't quite put it in a mixed format, unless you count 0 as its whole, then I guess we can say is
`0(9)/(16)=x`