let's firstly convert the mixed fractions to improper fractions.
now, 1¼ dozen of cupcakes.... well, let's keep in mind that a dozen has 12 units, so 1¼ dozen is then 12(1¼) cupcakes total.
[tex]\bf \stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}}~\hfill \stackrel{mixed}{1\frac{2}{3}}\implies \cfrac{1\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{5}{3}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \stackrel{\textit{how many cupcakes in }\frac{5}{4}\textit{ of a dozen?}}{12\cdot \cfrac{5}{4}\implies \cfrac{12}{4}\cdot 5\implies 15} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} cupcakes&\stackrel{cups}{flour}\\ \cline{1-2}\\ 15&\frac{5}{3}\\[1em] c&1 \end{array} \implies \cfrac{15}{c}=\cfrac{~~\frac{5}{3}~~}{1}\implies \cfrac{15}{c}=\cfrac{5}{3} \\\\\\ 45=5c\implies \cfrac{45}{5}=c\implies \boxed{9=c}[/tex]
Answer:
9 cupcakes
Step-by-step explanation:
Recipes are a combination of chemical and math concepts.
All need to be balanced, so you could change the number of cupcakes by divide the amount of each ingredient, following the proportion.
You can solve this with cross multiplication
1 2/3 cups are [tex]\frac{3}{3} +\frac{2}{3} =\frac{5}{3}[/tex] cups of flour.
If 5/3 cups made 15 cupcakes.
Then 1=3/3 cup made: [tex]X= (\frac{3}{3}15)/\frac{5}{3}[/tex]
So, X= 9 cupcakes
With 1 cup of flour, you can make 9 cupcakes.
