Mathematics, 04.06.2020 21:00 maualca

Jada has a scale map of Kansas that fits on a page in her book. The page is 5 inches by 8 inches. Kansas is about 210 miles by 410 miles. Select all scales that could be a scale of the map. (There are 2.54 centimeters in an inch.)

Answers: 2

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Answers

Answer from: briashia

E. cm to 200 Km

F. in to 100 mi

G. cm to 1,000 Km

Step-by-step explanation:

Verify each case

case A) in to mi

In this part the scale is equal to

$\frac{1}{1}\frac{in}{mi}$

Convert the actual dimensions of Kansas to the model dimensions on a map and compare with the dimensions of the page of the book

By proportion

$\frac{1}{1}\frac{in}{mi}=\frac{x}{210}\frac{in}{mi}\\ \\x=210\ in$

$\frac{1}{1}\frac{in}{mi}=\frac{x}{410}\frac{in}{mi}\\ \\x=410\ in$

The dimensions of Kansas on a map is greater than the dimensions of the page

therefore

case A) is not the solution

case B) cm to Km

In this part the scale is equal to

$\frac{1}{1}\frac{cm}{Km}$

Convert the dimensions of the book to cm

$1\ in=2.54\ cm$

$5\ in=5*2.54=12.70\ cm$

$8\ in=8*2.54=20.32\ cm$

Convert the actual dimensions of Kansas to Km

$1\ mi=1.609344\ Km$

$210\ mi=210*1.609344=337.96\ Km$

$410\ mi=410*1.609344=659.83\ Km$

Convert the actual dimensions of Kansas to the model dimensions on a map and compare with the dimensions of the page of the book

By proportion

$\frac{1}{1}\frac{cm}{km}=\frac{x}{337.96}\frac{cm}{km}\\ \\x=337.96\ cm$

$\frac{1}{1}\frac{cm}{km}=\frac{x}{659.83}\frac{cm}{km}\\ \\x=659.83\ cm$

The dimensions of Kansas on a map is greater than the dimensions of the page

therefore

case B) is not the solution

case C) in to mi

In this part the scale is equal to

$\frac{1}{10}\frac{in}{mi}$

Convert the actual dimensions of Kansas to the model dimensions on a map and compare with the dimensions of the page of the book

By proportion

$\frac{1}{10}\frac{in}{mi}=\frac{x}{210}\frac{in}{mi}\\ \\x=210/10=21\ in$

$\frac{1}{10}\frac{in}{mi}=\frac{x}{410}\frac{in}{mi}\\ \\x=410/10=41\ in$

The dimensions of Kansas on a map is greater than the dimensions of the page

therefore

case C) is not the solution

case D) ft to 100 mi

In this part the scale is equal to

$\frac{1}{100}\frac{ft}{mi}$

Convert the dimensions of the book to ft

$1\ ft=12\ in$

$5\ in=5/12=0.42\ ft$

$8\ in=8/12=0.67\ ft$

Convert the actual dimensions of Kansas to the model dimensions on a map and compare with the dimensions of the page of the book

By proportion

$\frac{1}{100}\frac{ft}{mi}=\frac{x}{210}\frac{ft}{mi}\\ \\x=210/100=2.1\ ft$

$\frac{1}{100}\frac{ft}{mi}=\frac{x}{410}\frac{ft}{mi}\\ \\x=410/100=4.1\ ft$

The dimensions of Kansas on a map is greater than the dimensions of the page

therefore

case D) is not the solution

case E) cm to 200 Km

In this part the scale is equal to

$\frac{1}{200}\frac{cm}{Km}$

Convert the dimensions of the book to cm

$1\ in=2.54\ cm$

$5\ in=5*2.54=12.70\ cm$

$8\ in=8*2.54=20.32\ cm$

Convert the actual dimensions of Kansas to Km

$1\ mi=1.609344\ Km$

$210\ mi=210*1.609344=337.96\ Km$

$410\ mi=410*1.609344=659.83\ Km$

Convert the actual dimensions of Kansas to the model dimensions on a map and compare with the dimensions of the page of the book

By proportion

$\frac{1}{200}\frac{cm}{km}=\frac{x}{337.96}\frac{cm}{km}\\ \\x=337.96/200=1.69\ cm$

$\frac{1}{200}\frac{cm}{km}=\frac{x}{659.83}\frac{cm}{km}\\ \\x=659.83/200=3.30\ cm$

The dimensions of Kansas on a map is less than the dimensions of the page

therefore

case E) could be a scale on the map

case F) in to 100 mi

In this part the scale is equal to

$\frac{1}{100}\frac{in}{mi}$

Convert the actual dimensions of Kansas to the model dimensions on a map and compare with the dimensions of the page of the book

By proportion

$\frac{1}{100}\frac{in}{mi}=\frac{x}{210}\frac{in}{mi}\\ \\x=210/100=2.1\ in$

$\frac{1}{100}\frac{in}{mi}=\frac{x}{410}\frac{in}{mi}\\ \\x=410/100=4.1\ in$

The dimensions of Kansas on a map is less than the dimensions of the page

therefore

case F) could be a scale on the map

case G) cm to 1,000 Km

In this part the scale is equal to

$\frac{1}{1,000}\frac{cm}{Km}$

Convert the dimensions of the book to cm

$1\ in=2.54\ cm$

$5\ in=5*2.54=12.70\ cm$

$8\ in=8*2.54=20.32\ cm$

Convert the actual dimensions of Kansas to Km

$1\ mi=1.609344\ Km$

$210\ mi=210*1.609344=337.96\ Km$

$410\ mi=410*1.609344=659.83\ Km$

Convert the actual dimensions of Kansas to the model dimensions on a map and compare with the dimensions of the page of the book

By proportion

$\frac{1}{1,000}\frac{cm}{km}=\frac{x}{337.96}\frac{cm}{km}\\ \\x=337.96/1,000=0.34\ cm$

$\frac{1}{1,000}\frac{cm}{km}=\frac{x}{659.83}\frac{cm}{km}\\ \\x=659.83/1,000=0.66\ cm$

The dimensions of Kansas on a map is less than the dimensions of the page

therefore

case G) could be a scale on the map

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