Solving Applications of Proportions
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. |