Answer
The steps are:
- Set up a proportion between antibiotic amount and body weight
- Cross multiply
- Solve for the unknown amount of antibiotic
- Check your answer
Work Step by Step
We explain the steps of Exercise 67.
First, we set up a proportion between the amount of the antibiotic and body weight. Since we know that $1\frac{1}{2}$ teaspoons is appropriate for 24 pounds of body weight, we can use this fact to determine the amount of the antibiotic for an $8$ pound infant. Thus the ratio is:
$\displaystyle \frac{1.5~teaspoons}{24~pounds}=\frac{n~teaspoons}{8~pounds}$
The next step is to cross multiply in order to solve for the unknown value $n$:
$1.5*8=24*n$
Next, we simplify and solve for $n$:
$12=24*n$
$n=\frac{12}{24}=\frac{1}{2}=0.5$ teapsoons
Thus we need to use $0.5$ teaspoons of antibiotic for the infant.
To check our answer, we note that $0.5$ is one-third ($\frac{1}{3}$) of $1\frac{1}{2}$. Similarly, 8 is $\frac{1}{3}$rd of 24. Thus our answer makes sense.
