Question

A certain drug is made from only two ingredients: compound A and compound B. There are 5 milliliters of compound A used for every 7 milliliters of compound B. If a chemist uses 270 milliliters of compound A, how many milliliters of the drug will be made?

Answer 1

`\bf \begin{array}{ccll}\stackrel{A}{mLs}&\stackrel{B}{mLs}\\\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\5&7\\270&b\end{array}\implies \cfrac{5}{270}=\cfrac{7}{b}\implies b=\cfrac{270\cdot 7}{5}\implies b=378\\\\\\\stackrel{\textit{mLs of the drug}}{A+B}\implies 270+378\implies 648`

now

Each marble bag sold by Laura's Marble Company contains 3 red marbles for every 5 blue marbles.

If a bag has 15 red marbles, how many blue marbles does it contain?

well, we know there are 3 red ones for every 5, so how many blue ones are there when there are 15 red ones?

`\bf \begin{array}{ccll}red&blue\\\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\3&5\\15&b\end{array}\implies \cfrac{3}{15}=\cfrac{5}{b}\implies b=\cfrac{15\cdot 5}{3}\implies b=25\\\\\\\stackrel{\textit{total marbles}}{red+blue}\implies 15+25`