Question

A certain drug is made from only two ingredients: compound A and compound B. There are 4 milliliters of compound A used for every 3 milliliters of compoundB. If a chemist wants to make 469 mililiters of the drug, how many milliliters of compound A are needed?

Answer 1

To answer this question we will set and solve a system of equations.

Let x be the number of milliliters of compound A that the chemist needs to make 469 milliliters and y be the number of milliliters of compound B, since there are 4 milliliters of compound A used for every 3 milliliters of compound B, then we can set the following system of equations:

$\begin{gathered} x+y=469, \\ \frac{x}{4}=\frac{y}{3}\text{.} \end{gathered}$

Multiplying the second equation by 4 we get:

$\begin{gathered} \frac{x}{4}\times4=\frac{y}{3}\times4, \\ x=\frac{4y}{3}\text{.} \end{gathered}$

Substituting the above equation in the first one we get:

$\frac{4y}{3}+y=469.$

Adding like terms we get:

$\frac{7y}{3}=469.$

Multiplying the above equation by 3/7 we get:

$\begin{gathered} \frac{7y}{3}\times\frac{3}{7}=469\cdot\frac{3}{7}, \\ y=201. \end{gathered}$

Finally, substituting y=201 at:

$x=\frac{4y}{3}$

we get:

$x=268.$

Answer: The chemist needs 268 milliliters of compound A.