Applications of Proportions Exercises
| Site: | Saylor Academy |
| Course: | RWM101: Foundations of Real World Math copy 1 |
| Book: | Applications of Proportions Exercises |
| Printed by: | Guest user |
| Date: | Wednesday, May 14, 2025, 2:08 AM |
Description
buttons.Applications of Proportions
Try these four problems. Read through the worked out solutions closely for any question you miss. Once you feel confident answering these types of questions, you are ready to move on to Unit 7.
1. On a road map, the scale indicates that \(1 \mathrm{~cm}\) represents \(60\) miles. If the measured distance between two cities on the map is \(6.7 \mathrm{~cm}\), how many miles apart are they?
2. Suppose a truck travels at \(55 \mathrm{mph}\). How many miles will the truck travel in \(8\) hours?
3. A recipe calls for \(3\) cups of milk for \(8\) servings. How many cups of milk are needed to make \(6\) servings?
4. At a local college, the cost per unit of instruction is \(\$24.00\). If a student plans to take \(27.5\) units during the next two semesters, how much will the student pay for tuition?
Source: Algebra2Go, https://www.saddleback.edu/faculty/Lperez/Algebra2Go/prealgebra/ratios/applpropHW.pdf
This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 License.
Answers
1. On a road map, the scale indicates that \(1 \mathrm{~cm}\) represents \(60\) miles. If the measured distance between two cities on the map is \(6.7 \mathrm{~cm}\), how many miles apart are they?
| \(\begin{align} \text { Proportion } \Longrightarrow \dfrac{1 \mathrm{~cm}}{60 \text { miles }}=\dfrac{6.7 \mathrm{~cm}}{\text {k miles }} \end{align}\) | |
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2. Suppose a truck travels at \(55 \mathrm{mph}\). How many miles will the truck travel in \(8\) hours?
| \( \text { Proportion } \Longrightarrow \dfrac{55 \text { miles }}{1 \text { hour }}=\dfrac{x \text { miles }}{8 \text { hours }} \) |
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| \( \begin{array}{r} 4 \, \, \, \\ 55\\ \times \quad 8 \\ \hline 440 \end{array} \) |
\( \begin{aligned} &\dfrac{55}{1}=\dfrac{x}{8} \\ \\ &440=x \\ \\ &\text { Therefore } x=440 \text { miles } \end{aligned} \) |
3. A recipe calls for \(3\) cups of milk for \(8\) servings. How many cups of milk are needed to make \(6\) servings?
| \(\text {Proportion}\Rightarrow \dfrac{3 \text { cups }}{8 \text { servings }}=\dfrac{x \text { cups }}{6 \text { servings}}\) | |
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\(\begin{aligned}&\dfrac{3}{8}=\dfrac{x}{6} \\ \\&\dfrac{18}{8}=\dfrac{8 x}{8} \\ \\ &\dfrac{18}{8}=x \\ &x=\dfrac{18 / 2}{8 / 2} \\ \\ &x=\dfrac{9}{4} \text { cups } \\ \\ &=\text { - or - } \\ \\&x=2 \dfrac{1}{4} \text { cups }\end{aligned}\) |
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4. At a local college, the cost per unit of instruction is \(\$24.00\). If a student plans to take \(27.5\) units during the next two semesters, how much will the student pay for tuition?
| \(\text {Proportion} \Rightarrow \dfrac{24 \text { dollars }}{1 \text { unit }}=\dfrac{x \text { dollars }}{27.5 \text { units }}\) | |
| \(\begin{align}\ \begin{array}{r} 27.5 \\\ \times 24 \\ \hline 1100 \\ +5500 \\ \hline 660.0 \end{array} \end{align}\) |
\( \begin{array}{l} \frac{24}{1}=\frac{x}{27.5} \\ \\ 660=x \\ 660=x \quad \text{Therefore} \quad x=660 \, \text{dollars} = \$ 660 \end{array} \) |