A chef uses 4(3/4) cups of broth for 10 servings of soup. How much broth is used in one serving of soup? Let x represent the amount of broth

Question
A chef uses \(\displaystyle{4}{\left(\frac{{3}}{{4}}\right)}\) cups of broth for 10 servings of soup. How much broth is used in one serving of soup? Let x represent the amount of broth

Answers (1)

2020-11-28
Using the equivalent ratio, we cross multiply:
\(\displaystyle\frac{{{4}{\left(\frac{{3}}{{4}}\right)}}}{{10}}=\frac{{x}}{{1}}\)
\(\displaystyle{4}{\left(\frac{{3}}{{3}}\right)}{\left({1}\right)}={10}{x}\)
\(\displaystyle{4}{\left(\frac{{3}}{{4}}\right)}={10}{x}\)
Write the mixed number as an importer fraction:
\(\displaystyle\frac{{19}}{{4}}={10}{x}\)
Multiply both sides by \(\displaystyle\frac{{1}}{{10}}\):
\(\displaystyle{\left(\frac{{19}}{{4}}\right)}\cdot{\left(\frac{{1}}{{10}}\right)}={10}{x}\cdot\frac{{1}}{{10}}\)
\(\displaystyle\frac{{19}}{{40}}={x}\)
So, there is \(\displaystyle\frac{{19}}{{40}}\) cup of broth per serving.
\(\displaystyle\frac{{19}}{{40}}\) cup
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