Yulia

2021-08-20

Recommended dosages. The recommended dosage of a medication is 250 mg per 110 pounds of body weight. Find the dosage for a person weighing 176 pounds.

hajavaF

To find:
The dosage for a person weighing 176 pounds.
Proportion:
An equation which indicating the two ratios are equal is called proportion. In the proportion $\frac{a}{b}=\frac{c}{d}$, the numbers a and d are called the extremes, and the numbers b and c are called the means.
Property of proportions
In any proportion, the product of the extremes is equal to the product of the means.
Calculation:
It is given that the dosage of a medication is 250 mg per 110 pounds of body weight.
Find the dosage for a person weighing 176 pounds.
Let x represent the number of dosage for a person weighing 176 pounds.
The ratio of the dosage of a medication 250 mg per 110 pounds is $\frac{250}{110}$.
The ratio of the dosage of a medication x mg per 176 pounds is $\frac{x}{176}$.
The proportion is $\frac{250}{110}=\frac{x}{176}$.
Here, the means are x and 110 and the extremes are 250 and 176.
Use property of proportions to solve $\frac{250}{110}=\frac{x}{176}$ for x.
The product of the extremes equals the product of the means.
$\left(250\right)\left(176\right)=x\left(110\right)$
Remove parenthesis and simplify.
$\frac{250×176}{110}=x$
$x=\frac{25×176}{11}$
$x=400$
Therefore, the dosage for a person weighing 176 pounds is 400 mg.
Final statement:
The dosage for a person weighing 176 pounds is 400 mg.

Jeffrey Jordon

Answer is given below (on video)

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