Algebraic Equations and Inequalities Word problem on proportions: Problem type 2 A certain drug is made from only two ingredients: compound A and compound B. There are 7 milliliters of compound A used for every 4 milliliters of compound B. If a chemist wants to make 1001 milliliters of the drug, how many milliliters of compound $A$ are needed? milliliters of compound A

Step 1 ：A certain drug is made from only two ingredients: compound A and compound B. There are 7 milliliters of compound A used for every 4 milliliters of compound B. If a chemist wants to make 1001 milliliters of the drug, how many milliliters of compound A are needed?

Step 2 ：We can solve for the amount of compound A needed by cross multiplying and dividing. The ratio of compound A to compound B is \( \frac{7}{4} = 1.75 \).

Step 3 ：Let's denote the total amount of the drug as 1001 milliliters.

Step 4 ：We can calculate the amount of compound A needed using the formula: \( \text{compound A} = \frac{\text{ratio of A to B} \times \text{total drug}}{1 + \text{ratio of A to B}} \).

Step 5 ：Substituting the given values into the formula, we get: \( \text{compound A} = \frac{1.75 \times 1001}{1 + 1.75} = 637.0 \) milliliters.

Step 6 ：Final Answer: The chemist needs \(\boxed{637}\) milliliters of compound A to make 1001 milliliters of the drug.