Question

I an confused on how to get to 6 cups

Answer 1

Answer: 4 tablespoons of kernels.

Step-by-step explanation: Use proportions, so (1 1/2)/(2 1/4) = x/6.

You would do (1 1/2) * 6 = 9 (or 3/2 * 6). And then 9 / (2 1/4) (or 9 * 4/9 because of keep change flip) and get 4. 36/9 = 4.

Answer 2

let's firstly convert the mixed fractions to improper fractions.

`\stackrel{mixed}{2(1)/(4)}\implies \cfrac{2\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{9}{4}}~\hfill \stackrel{mixed}{1(1)/(2)} \implies \cfrac{1\cdot 2+1}{2} \implies \stackrel{improper}{\cfrac{3}{2}} \\\\[-0.35em] ~\dotfill`

`\begin{array}{ccll} \stackrel{popcorn}{cups}&\stackrel{tspoons}{kernel}\\ \cline{1-2} (9)/(4)&(3)/(2)\\[1em] 6&x \end{array}\implies \cfrac{~~ ( 9 )/( 4 ) ~~}{6}~~ = ~~\cfrac{~~ ( 3 )/( 2 ) ~~}{x}\implies \cfrac{~~ ( 9 )/( 4 ) ~~}{(6)/(1)}~~ = ~~\cfrac{~~ ( 3 )/( 2 ) ~~}{(x)/(1)} \\\\\\ \cfrac{9}{4}\cdot \cfrac{1}{6}=\cfrac{3}{2}\cdot \cfrac{1}{x}\implies \cfrac{9}{24}=\cfrac{3}{2x}\implies \cfrac{3}{8}=\cfrac{3}{2x} \\\\\\ 6x=24\implies x=\cfrac{24}{6}\implies \boxed{x=4}`