Question

11 help cause I'm stuck
:3
11 ​

Answer 1

let's say each restaurant has a container of soup which is the same size, let's say there is a total of "s" amount of soup in the container of each restaurant, so 5/4 of that much will just be (5/4)s and 7/4 of "s" is just (7/4)s.

well, one restaurant makes 20 servings from 5/4 of it and the other makes 25 from 7/4 of it,

`\bf \cfrac{5}{4}s/ 20\implies \cfrac{5}{4}s/ \cfrac{20}{1}\implies \cfrac{~~\begin{matrix} 5 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{4}s\cdot \cfrac{1}{\underset{4}{~~\begin{matrix} 20 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\implies \boxed{\cfrac{1}{16}}s \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{4}s/ 25\implies \cfrac{7}{4}s/ \cfrac{25}{1}\implies \cfrac{7}{4}s\cdot \cfrac{1}{25}\implies \boxed{\cfrac{7}{100}}s`

now, which one is larger? well, we can simply put both fractions with the same denominator by multiplying one by the other's denominator,

`\bf \cfrac{1}{16}\cdot \cfrac{100}{100}\implies \boxed{\cfrac{100}{1600}}\qquad \qquad \qquad \stackrel{\textit{\Large larger}}{\cfrac{7}{100}\cdot \cfrac{16}{16}\implies \boxed{\cfrac{112}{1600}}}`