Question

A 6.0 ounce cup of coffee contains 50 mg of caffeine. Please calculate the percentage of caffeine in the coffee.

Answer 1

In 6 ounces of coffee, there are 50 mg of caffeine

In 1 ounce of coffee there are 50/6 mg of caffeine or 8.33 mg caffeine

8.33 is equivalent to 83.3%

Answer 2

Hmm let's convert the mg to ounces

so.. there are 28.35 mgs in 1oz, how many oz in 50?

$\bf \begin{array}{ccllll} oz&mg\\ \textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\ 1&28.35\\ x&50 \end{array}\implies \cfrac{1}{x}=\cfrac{28.35}{50}\implies \cfrac{50}{28.35}=x\implies \cfrac{1000}{567}=x$

now, if 6oz is the 100%, how much is it then, 1000/576 oz in percentage?

well  $\bf \begin{array}{ccllll} amount&\%\\ \textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\ 6&100\\ \frac{1000}{567}&x \end{array}\implies \cfrac{6}{\frac{1000}{567}}=\cfrac{100}{x}\implies \cfrac{\frac{6}{1}}{\frac{1000}{567}}=\cfrac{100}{x} \\\\\\ \cfrac{6\cdot 567}{1000}=\cfrac{100}{x}\implies x=\cfrac{100000}{3402}\implies x\approx 29.39\%$