Applications of Proportions Exercises

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}

\(\begin{align} \text { Proportion } \Longrightarrow \dfrac{1 \mathrm{~cm}}{60 \text { miles }}=\dfrac{6.7 \mathrm{~cm}}{\text {k miles }} \end{align}\)
\( \begin{array}{r} 4 \, \, \, \, \\ 6.7 \\ \times 60 \\ \hline 402.0 \end{array} \)	\( \begin{aligned} &\dfrac{1}{60}=\dfrac{6.7}{x} \qquad \qquad LCD=10 \\ \\ &\dfrac{1}{60}=\dfrac{10(6.7)}{10(x)} \\ \\ &\dfrac{1}{60}=\dfrac{67}{10 x} \\ \\ &10 x=402 \\ \\ &\dfrac{10 x}{10} =\dfrac{402}{10} \\ \\ &x=40.2 \text { miles } \end{aligned} \)

\( \text { Proportion } \Longrightarrow \dfrac{55 \text { miles }}{1 \text { hour }}=\dfrac{x \text { miles }}{8 \text { hours }} \)
\( \begin{array}{r} 4 \, \, \, \\ 55\\ \times \quad 8 \\ \hline 440 \end{array} \)	\( \begin{aligned} &\dfrac{55}{1}=\dfrac{x}{8} \\ \\ &440=x \\ \\ &\text { Therefore } x=440 \text { miles } \end{aligned} \)

\(\text {Proportion}\Rightarrow \dfrac{3 \text { cups }}{8 \text { servings }}=\dfrac{x \text { cups }}{6 \text { servings}}\)
\(\begin{aligned}&\dfrac{3}{8}=\dfrac{x}{6} \\ \\&\dfrac{18}{8}=\dfrac{8 x}{8} \\ \\ &\dfrac{18}{8}=x \\ &x=\dfrac{18 / 2}{8 / 2} \\ \\ &x=\dfrac{9}{4} \text { cups } \\ \\ &=\text { - or - } \\ \\&x=2 \dfrac{1}{4} \text { cups }\end{aligned}\)