Use the information below:

[tex]\[ D = \frac{a}{a+12} \cdot M \][/tex]

where:
- [tex]\( D \)[/tex] = child's dosage in milligrams
- [tex]\( a \)[/tex] = age of the child
- [tex]\( M \)[/tex] = adult dosage in milligrams

If the adult dosage of the medicine is 180 milligrams (mg), what is [tex]\(\frac{1}{3}\)[/tex] of the adult dose?

(Show your work).



Answer :

To determine [tex]\(\frac{1}{3}\)[/tex] of the adult dosage, follow these steps:

1. Identify the adult dosage ([tex]\(M\)[/tex]):
[tex]\[ M = 180 \text{ mg} \][/tex]

2. Calculate [tex]\(\frac{1}{3}\)[/tex] of the adult dosage:
To do this, we multiply the adult dosage by [tex]\(\frac{1}{3}\)[/tex].

[tex]\[ \text{One-third dosage} = \frac{1}{3} \times M \][/tex]

Substituting the value of [tex]\(M\)[/tex]:
[tex]\[ \text{One-third dosage} = \frac{1}{3} \times 180 \text{ mg} \][/tex]

3. Perform the multiplication:
[tex]\[ \text{One-third dosage} = \frac{180}{3} \text{ mg} \][/tex]

4. Complete the division:
[tex]\[ \frac{180}{3} = 60 \text{ mg} \][/tex]

Thus, [tex]\(\frac{1}{3}\)[/tex] of the adult dosage of 180 milligrams is [tex]\(\boxed{60 \text{ mg}}\)[/tex].