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Question Find the quantity of compound A needed to make 648 milliliters of a drug, given that the drug is made from 5 milliliters of compound A for every 3 milliliters of compound B.
53\frac{5}{3} milliliters of compound A are used for every milliliter of the drug. To make 648 milliliters, the amount of compound A required is 53×648\frac{5}{3} \times 648 milliliters.

Studdy Solution

STEP 1

Assumptions1. The drug is made from only two ingredients compound A and compound B. There are5 milliliters of compound A used for every3 milliliters of compound B3. The chemist wants to make648 milliliters of the drug

STEP 2

First, we need to find the ratio of compound A to the total volume of the drug. We can do this by dividing the volume of compound A by the total volume of both compounds.
RatioA=VolumeAVolumeA+VolumeBRatio_{A} = \frac{Volume_{A}}{Volume_{A} + Volume_{B}}

STEP 3

Now, plug in the given values for the volumes of compound A and compound B to calculate the ratio of compound A.
RatioA=55+3Ratio_{A} = \frac{5}{5 +3}

STEP 4

Calculate the ratio of compound A.
RatioA=8Ratio_{A} = \frac{}{8}

STEP 5

Now that we have the ratio of compound A, we can find the volume of compound A needed to make the drug. This can be done by multiplying the total volume of the drug by the ratio of compound A.
VolumeA=Total volumetimesRatioAVolume_{A} = Total\, volume \\times Ratio_{A}

STEP 6

Plug in the values for the total volume and the ratio of compound A to calculate the volume of compound A.
VolumeA=648times58Volume_{A} =648 \\times \frac{5}{8}

STEP 7

Calculate the volume of compound A.
VolumeA=648times5=405Volume_{A} =648 \\times \frac{5}{} =405405 milliliters of compound A are needed to make648 milliliters of the drug.

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