Example 6.45

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.


Example 6.46

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.


Example 6.47

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.
Back to '6.4 Applications of Proportions'