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On a scale map 0.7 cm represents 8.4 km. if the distance between two points on the map is 4.65cm, what is the actual distance between the points?

Last updated date: 19th Jun 2024
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Hint: We solve this by converting the word problem into proportions. Given 0.7 cm represents 8.4 km. 46.5 cm represents ‘x’ km. It can represent in proportions as \[0.7:4.65 = 8.4:x\] . A proportion is an equation that says that two ratios are equivalent. If one number in a proportion is unknown you can find that number by solving the proportion.

Complete step-by-step answer:
We converted the word problem into proportion.
We have, \[0.7:4.65 = 8.4:x\]
My first step will be to convert the colon based odds notation to fractional form, so I get an equation with two fractions which we can solve easily. As we have only one unknown variable value among the four values, we can solve this.
 \[ \Rightarrow \dfrac{{0.7}}{{4.65}} = \dfrac{{8.4}}{x}\]
Since the unknown value is in the denominator, take the reciprocal of the above equation.
 \[ \Rightarrow \dfrac{{4.65}}{{0.7}} = \dfrac{x}{{8.4}}\]
Multiply 8.4 on both sides,
 \[ \Rightarrow \dfrac{{4.65}}{{0.7}} \times 8.4 = \dfrac{x}{{8.4}} \times 8.4\]
On cancelling and rearranging the terms we get,
 \[ \Rightarrow x = \dfrac{{4.65}}{{0.7}} \times 8.4\]
 \[ \Rightarrow x = 46.5 \times 1.2\]
 \[ \Rightarrow x = 55.8\]
Thus we have 55.8 km.
So, the correct answer is “Option B”.

Note: You can write mathematical proportions in two ways. You can compare the numbers with colons, or you can write the proportion in the form of equivalent fraction. If the unknown is in the numerator. We can solve it easily. If the unknown is in the denominator we take reciprocal of the whole equation as done above or we can use a method that involves cross product. The cross product is the product of one of the ratios and the denominator of the second ratio.