QuestionA drug uses 3 mL of compound A for every 5 mL of compound B. How much A is needed for 544 mL of the drug?

Studdy Solution

STEP 1

Assumptions1. The drug is made from only two ingredients compound A and compound B. . There are3 milliliters of compound A used for every5 milliliters of compound B.
3. The chemist wants to make544 milliliters of the drug.
4. The ratio of compound A to compound B is constant for any amount of the drug.

STEP 2

We need to find the total amount of compound A needed to make544 milliliters of the drug. We can start by finding the ratio of compound A to the total amount of the drug.
$Ratio_{A} = \frac{Compound_{A}}{Compound_{A} + Compound_{B}}$

STEP 3

Now, plug in the given values for compound A and compound B to find the ratio.
$Ratio_{A} = \frac{3 ml}{3 ml +5 ml}$

STEP 4

Calculate the ratio of compound A to the total amount of the drug.
$Ratio_{A} = \frac{3 ml}{8 ml}$

STEP 5

Now that we have the ratio of compound A, we can find the amount of compound A needed to make544 milliliters of the drug. We do this by multiplying the total amount of the drug by the ratio of compound A.
$Amount_{A} = Total\, drug\, amount \\times Ratio_{A}$

STEP 6

Plug in the values for the total drug amount and the ratio of compound A to calculate the amount of compound A.
$Amount_{A} =544 ml \\times \frac{3 ml}{8 ml}$

STEP 7

Calculate the amount of compound A needed.
$Amount_{A} =544 ml \\times \frac{3 ml}{ ml} =204 ml$ The chemist needs204 milliliters of compound A to make544 milliliters of the drug.

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