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, \\ (x)/(4)=(y)/(3)\text{.} \end{gathered}`

Multiplying the second equation by 4 we get:

`\begin{gathered} (x)/(4)*4=(y)/(3)*4, \\ x=(4y)/(3)\text{.} \end{gathered}`

Substituting the above equation in the first one we get:

`(4y)/(3)+y=469.`

Adding like terms we get:

`(7y)/(3)=469.`

Multiplying the above equation by 3/7 we get:

`\begin{gathered} (7y)/(3)*(3)/(7)=469\cdot(3)/(7), \\ y=201. \end{gathered}`

Finally, substituting y=201 at:

`x=(4y)/(3)`

we get:

`x=268.`

Answer: The chemist needs 268 milliliters of compound A.