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3 years ago

Morganville and Newton are 45 miles apart. On a map, the two cities are 3 inches apart. What is the map scale?

Mathematics

1 answer:

dolphi86 [110]3 years ago

8 0

45 miles/3 in=15miles/1 inch

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harina [27]

Given:

$a=1.6,b=\dfrac{1}{-2},c=\dfrac{-5}{-7}$

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$a(b-c)=ab-ac$ for the given values.

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We need to verify $a(b-c)=ab-ac$ .

Taking left hand side, we get

$a(b-c)=1.6\left(\dfrac{1}{-2}-\dfrac{-5}{-7}\right)$

$a(b-c)=1.6\left(-\dfrac{1}{2}-\dfrac{5}{7}\right)$

Taking LCM, we get

$a(b-c)=1.6\left(\dfrac{-7-10}{14}\right)$

$a(b-c)=\dfrac{16}{10}\left(\dfrac{-17}{14}\right)$

$a(b-c)=\dfrac{8}{5}\left(\dfrac{-17}{14}\right)$

$a(b-c)=-\dfrac{68}{35}\right)$

Taking right hand side, we get

$ab-ac=1.6\times \dfrac{1}{-2}-1.6\times \dfrac{-5}{-7}$

$ab-ac=-\dfrac{16}{20}-\dfrac{8}{7}$

$ab-ac=-\dfrac{4}{5}-\dfrac{8}{7}$

Taking LCM, we get

$ab-ac=\dfrac{-28-40}{35}$

$ab-ac=\dfrac{-68}{35}$

Now,

$LHS=RHS$

Hence proved.

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3 years ago