Applications of Proportions Exercises
buttons.Applications of Proportions
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?
| \(\text {Proportion} \Rightarrow \dfrac{24 \text { dollars }}{1 \text { unit }}=\dfrac{x \text { dollars }}{27.5 \text { units }}\) | |
| \(\begin{align}\ \begin{array}{r} 27.5 \\\ \times 24 \\ \hline 1100 \\ +5500 \\ \hline 660.0 \end{array} \end{align}\) |
\( \begin{array}{l} \frac{24}{1}=\frac{x}{27.5} \\ \\ 660=x \\ 660=x \quad \text{Therefore} \quad x=660 \, \text{dollars} = \$ 660 \end{array} \) |