# 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

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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