Q7. - Algebra 1

Question

The scale on a map shows that $\mathbf{1}\mathbf{.}\mathbf{5}$ centimeters is equivalent to 40 miles. If the distance on the map between two cities in 8 centimeters, about how many miles apart are the cities?

$\mathit{A}$  178 miles

          

$\mathit{B}$  213 miles

$\mathit{C}$  224 miles

$\mathit{D}$  275 miles

Step-by-Step Solution

Answer

The cities are 213 miles apart. Option $\mathit{B}$ is correct.

Step 1. State the rule of ‘cross multiplication’.

If two ratios are equal, then the numerator of first fraction is multiplied by the denominator of second fraction and the numerator of second fraction is multiplied by the denominator of first fraction.

That is, if $\frac{a}{b}=\frac{c}{d}$ then $ad=cb$.

Step 2. Find the distance.

The scale on a map shows that $1.5$ centimeters is equivalent to 40 miles.  

That is, $1.5$ centimeters=40 miles.

Therefore, 1 centimeter $=\frac{40}{1.5}$miles.

The cities are 8 centimeters apart.

Therefore the distance($d$) between the cities is given as:

 $\begin{array}{l}d=\frac{40}{1.5}\times 8\\ =\frac{320}{1.5}\\ =213.33\\ \approx 213\end{array}$

Step 3. State the conclusion.

Therefore, the distance between the two cities is approximately 213 miles.

Option $B$ is correct.