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}

\begin{array}{r}4 \, \, \, \, \\6.7 \\\times 60 \\\hline 402.0\end{array}

 \begin{aligned}&\dfrac{1}{60}=\dfrac{6.7}{x} \qquad \qquad LCD=10 \\\\&\dfrac{1}{60}=\dfrac{10(6.7)}{10(x)} \\\\&\dfrac{1}{60}=\dfrac{67}{10 x} \\\\&10 x=402 \\\\&\dfrac{10 x}{10} =\dfrac{402}{10} \\\\ &x=40.2 \text { miles }\end{aligned}

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 }}
\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}}

\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}

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}

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