Let’s practice using reasoning, proportion, and dosage formulas in medication calculations with a few more examples.

The patient has been prescribed a dose of 470 000 IU of penicillin. The concentration of the drug solution you are using is 300 000 IU/ml. How many milliliters of solution will you give the patient?[br][br]Calculate the dose to be administered to the patient using both the proportion and the dosage formula and then check the result by reasoning.[br][br][br][size=150]Proportion:[/size][br][br][table][tr][td][/td][td]active substance (IU)[/td][td]solution (ml)[/td][/tr][tr][td]in a bottle[/td][td]300 000[/td][td]1[/td][/tr][tr][td]given to the patient[/td][td]470 000[/td][td]x[/td][/tr][/table][br]Let's solve the comparison by cross-referencing:[br][br]1. Multiply the numerator (superscript) of the first ratio by the denominator (subscript) of the second ratio, and also the denominator of the first ratio by the numerator of the second ratio. Both inputs give the same value, resulting in a new equation that is the same as the original equation.[br][br][math]\begin{array}{lrcll}[br]\space \space \frac{300 \space 000}{470 \space 000}=\frac{1}{x}\\[br]\space \\[br]\space \space 300 \space 000 \cdot x = 470 \space 000 \cdot 1[br]\end{array}[/math][br][br]2.Divide the equation by the coefficient of the unknown variable.[br][br][math]\begin{array}{lrcll}[br]& 300 \space 000 \cdot x&=&470 \space 000&|:300 \space 000\\[br]& x&=&\frac{470 \space 000}{300 \space 000}&\\ [br]&x& =& 1,56666666667& [br]\end{array}[/math][br][br]The result is 1.5 ml of medicine, because medicine invoices usually round down.[br][br][br][size=150]Dosage formula:[/size][br][br][math]\text{Dose}=\frac{\text{the amount of active substance prescribed for the patient}}{\text{concentration of the solution}}[/math][br][br][math]\text{Dose}=\frac{\text{470 000}}{\text{300 000}}[/math][br][br][math]\text{Dose}=1,56666666667[/math][br][br]The result is therefore, as above, a rounded dose of 1.5 millilitres of medicine. The patient is therefore given 1.5 ml. [br][br][size=150]Check the result of the calculations by reasoning:[/size][br][br][table][tr][td]solution (ml)[/td][td]active substance (IU)[/td][/tr][tr][td]1[/td][td]300 000[/td][/tr][tr][td]0,5[/td][td]150 000[/td][/tr][tr][td]1,5[/td][td]450 000[/td][/tr][tr][td]0,1[/td][td]30 000[/td][/tr][tr][td]1,6[/td][td]480 000[/td][/tr][/table][br]By deduction, the amount of solution to be administered is between 1.5 and 1.6 millilitres. We can therefore be confident of the result.[br][br][br][br][br][br][br][br][br]

The patient has been prescribed paracetamol 250 mg four times a day. A 24 mg/ml paracetamol solution is available. How many millilitres of solution do you give the patient at a time?[br][br]Calculate the single dose for the patient using a dose formula and a ratio:[br][br][size=150]Dosage formula:[/size][br][br][math]\text{Dose}=\frac{\text{the amount of active substance prescribed for the patient}}{\text{concentration of the solution}}[/math][br][br][math]\text{Dose}=\frac{\text{250}}{\text{24}}[/math][br][br][math]\text{Dose}={\text{10,41666667}[/math][br][br][math]\text{Dose}={\text{10,4}[/math][br][br][size=150][br]Proportion:[/size][br][br][table][tr][td][/td][td]active substance (mg)[/td][td]solution (ml)[/td][/tr][tr][td]in the bottle[/td][td]24[/td][td]1[/td][/tr][tr][td]given to the patient[/td][td]250[/td][td]x[/td][/tr][/table][br]Let's solve the equation:[br][br]1. Cross-referencing.[br][br][math]\begin{array}{lrcll}[br]\space \space \frac{24}{250}=\frac{1}{x}\\[br]\space \\[br]\space \space 24 \cdot x = 250 \cdot 1[br]\end{array}[/math][br][br]2. Solving the unknown.[br][br][math]\begin{array}{lrcll}[br]& 24x&=&250&|:24\\[br]& x&=&\frac{250}{24}&\\ [br]&x& =& 10,41666667& [br]\end{array}[/math][br][br][br]This gives a rounded result of a single dose of 10.4 millilitres of medicine. [br][br][size=150][br]Check the result of the calculations by reasoning:[/size][br][br][table][tr][td]solution (ml)[/td][td]active substance (mg)[/td][/tr][tr][td]1[/td][td]24[/td][/tr][tr][td]10[/td][td]240[/td][/tr][tr][td]11[/td][/tr][/table][br]The amount of paracetamol solution given to the patient should be between 10 and 11 millilitres, so 10.4 millilitres is a reasonable result.[br][br][br][br][br]