Solving Applications of Proportions

Identify what you are asked to find.	How many ml of acetaminophen the doctor will prescribe
Choose a variable to represent it.	Let $a=\mathrm{ml}$ of acetaminophen.
Write a sentence that gives the information to find it.	If $5$ ml is prescribed for every $25$ pounds, how much will be prescribed for $80$ pounds?
Translate into a proportion.	$\dfrac{\mathrm{ml}}{\text { pounds }}=\dfrac{\mathrm{ml}}{\text { pounds }}$
Substitute given values - be careful of the units.	$\dfrac{5}{25}=\dfrac{a}{80}$
Multiply both sides by $80$ .	$80 \cdot \dfrac{5}{25}=80 \cdot \dfrac{a}{80}$
Multiply and show common factors.	$\dfrac{16 \cdot 5 \cdot 5}{5 \cdot 5}=\dfrac{80 a}{80}$
Simplify.	$16=a$
Check if the answer is reasonable.
Yes. Since $80$ is about $3$ times $25$ , the medicine should be about $3$ times $5$ .
Write a complete sentence.	The pediatrician would prescribe $16$ ml of acetaminophen to Zoe.

You could also solve this proportion by setting the cross products equal.

Identify what you are asked to find.	How many calories are in a whole bag of microwave popcorn?
Choose a variable to represent it.	Let $c= \text{number of calories}$ .
Write a sentence that gives the information to find it.	If there are $120$ calories per serving, how many calories are in a whole bag with $3.5$ servings?
Translate into a proportion.	$\dfrac{\text { calories }}{\text { serving }}=\dfrac{\text { calories }}{\text { serving }}$
Substitute given values.	$\dfrac{120}{1}=\dfrac{c}{3.5}$
Multiply both sides by $3.5$ .	$(3.5)\left(\dfrac{120}{1}\right)=(3.5)\left(\dfrac{c}{3.5}\right)$
Multiply.	$420=c$
Check if the answer is reasonable.
Yes. Since $3.5$ is between $3$ and $4$ , the total calories should be between $360 (3⋅120)$ and $480 (4⋅120)$ .
Write a complete sentence.	The whole bag of microwave popcorn has 420 calories.

Identify what you are asked to find.	How many Mexican pesos did Josiah get?
Choose a variable to represent it.	Let $p=\text{number of pesos}$ .
Write a sentence that gives the information to find it.	If $\$1$ U.S. is equal to $12.54$ Mexican pesos, then $\$325$ is how many pesos?
Translate into a proportion.	$\dfrac{\$}{\text { pesos }}=\dfrac{\$}{\text { pesos }}$
Substitute given values.	$\dfrac{1}{12.54}=\dfrac{325}{p}$
The variable is in the denominator, so find the cross products and set them equal.	$p \cdot 1=12.54(325)$
Simplify.	$c=4,075.5$
Check if the answer is reasonable.
Yes, $\$100$ would be $$1,254$ pesos. $\$325$ is a little more than $3$ times this amount.
Write a complete sentence.	Josiah has $4075.5$ pesos for his spring break trip.