A certain drug is made from only two ingredients: compound A and compound B. There are 5 milliliters of compound A used for every 4 milliliters of compound B. If a chemist wants to make 612 milliliters of the drug, how many milliliters of compound B are needed?

We are given that the drug is made from two ingredients, compound A and compound B, in a ratio of 5:4. The total volume of the drug the chemist wants to make is 612 milliliters.

Let \( x \) be the amount of compound B needed.

The ratio of compound A to compound B is:

\[
\frac{\text{Compound A}}{\text{Compound B}} = \frac{5}{4}
\]

This implies that for every 5 milliliters of compound A, there are 4 milliliters of compound B. The total amount of the drug is the sum of the amounts of compound A and compound B:

\[
\text{Compound A} + \text{Compound B} = 612 \, \text{milliliters}
\]

Using the ratio, the amount of compound A is \( \frac{5}{4} \times x \). So, we can set up the equation for the total amount of the drug:

\[
\frac{5}{4}x + x = 612
\]

Now, let's solve for \( x \):

\[
\frac{5}{4}x + \frac{4}{4}x = 612
\]

\[
\frac{9}{4}x = 612
\]

Multiply both sides by 4 to eliminate the fraction:

\[
9x = 2448
\]

Now, divide by 9:

\[
x = \frac{2448}{9} = 272
\]

Thus, the chemist needs **272 milliliters** of compound B.

Would you like a detailed explanation of any steps or have further questions?

Here are 5 related questions to extend your understanding:
1. How many milliliters of compound A are required in the same scenario?
2. If the chemist wanted to make 918 milliliters of the drug, how much compound B would be needed?
3. What is the total amount of compound A and B required for 100 milliliters of the drug?
4. How would the formula change if the ratio of compound A to B was 3:2?
5. What would happen to the required amount of compound B if the total volume of the drug was doubled?

**Tip:** Always check if your ratio correctly matches the problem when dealing with mixtures.

A certain drug is made from only two ingredients: compound A and compound B. There are 5 milliliters of compound A used for every 4 milliliters of compound B. If a chemist wants to make 612 milliliters of the drug, how many milliliters of compound B are needed?

Learn how to calculate the required milliliters of compound B in a drug mixture using a 5:4 ratio. In this example, a chemist needs to make 612 milliliters of the drug. This step-by-step solution explains how to apply ratios and algebraic equations to solve the problem. Suitable for Grades 6-8.

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