A pharmacist is to prepare 30 milliliters of a solution with a drug concentration of 2 mg/mL. To do so,
he will mix a solution with a drug concentration of 7 mg/mL with grape-flavored syrup. If ๐ฅ represents
the number of milliliters of grape-flavored syrup needed, find the value of ๐ฅ.
make sure the amount of drug adds up:
7(30-x) + 0x = 2(30)
Drug needed in 30ml at 2mg/ml =2mg*30 which is 60mg. Therefore number of ml at 7mg/ml =60mg/7mg. So the answer is 8.5ml of grape syrup. Conclussion: The value of โนโน is 8.5
To find the value of ๐ฅ, we need to set up an equation using the given information.
Let's break down the problem step by step:
The pharmacist wants to prepare a 30 mL solution with a drug concentration of 2 mg/mL.
He has a solution with a drug concentration of 7 mg/mL that he will mix with grape-flavored syrup.
The pharmacist will mix ๐ฅ milliliters of grape-flavored syrup with the solution to achieve the desired concentration.
Let's calculate the amount of drug in the solution and the amount of drug in the grape-flavored syrup:
Amount of drug in the solution = 30 mL ร 2 mg/mL = 60 mg
Amount of drug in the grape-flavored syrup = ๐ฅ mL ร 0 mg/mL (since grape-flavored syrup doesn't contain the drug)
Now, the total amount of drug in the final mixture should be equal to the sum of the drug amounts in the solution and the grape-flavored syrup.
Total amount of drug = Amount of drug in the solution + Amount of drug in the grape-flavored syrup
Total amount of drug = 60 mg + 0 mg = 60 mg
Since we know the concentration of the solution to be 7 mg/mL, we can set up the equation:
Total amount of drug = Concentration ร Volume of the mixture
60 mg = 7 mg/mL ร (๐ฅ mL + 30 mL)
Now, let's solve the equation for ๐ฅ:
60 mg = 7 mg/mL ร (๐ฅ mL + 30 mL)
Divide both sides of the equation by 7 mg/mL:
60 mg / 7 mg/mL = ๐ฅ mL + 30 mL
(60/7) mL = ๐ฅ mL + 30 mL
8.57 mL = ๐ฅ mL + 30 mL
Now, let's isolate ๐ฅ:
8.57 mL - 30 mL = ๐ฅ mL
-21.43 mL = ๐ฅ mL
Therefore, the value of ๐ฅ is -21.43 mL.
However, it is not physically possible to have a negative volume of grape-flavored syrup. So, in this case, there must be an error in the calculation or the given information. Please double-check the problem and the values provided.