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oksano4ka [1.4K]
3 years ago
9

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 4

10 miles. Select all scales that could be a scale on the map. (There are 2.54 centimeters in an inch.)
A. 1 in to 1 my
B. 1 cm to 1 km
C. 1 in to 10 mi
D. 1 ft to 100 mi
E. 1 cm to 200 km
F. 1 in to 100 mi
G. 1 cm to 1000 km
Mathematics
2 answers:
malfutka [58]3 years ago
7 0

Answer:

E. 1 cm to 200 Km

F. 1 in to 100 mi

G. 1 cm to 1,000 Km

Step-by-step explanation:

Verify each case

case A) 1 in to 1 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) 1 cm to 1 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

so

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

so

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) 1 in to 10 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) 1 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

so

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) 1 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

so

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

so

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) 1 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) 1 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

so

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

so

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

Semenov [28]3 years ago
3 0
I think the letter is b
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