Question

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 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

Answer 1

I think the letter is b

Answer 2

E.
`1` cm to
`200` Km

F.
`1` in to
`100` mi

G.
`1` cm to
`1,000` Km

Explanation:

Verify each case

case A)
`1` in to
`1` mi

In this part the scale is equal to

`(1)/(1)(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

`(1)/(1)(in)/(mi)=(x)/(210)(in)/(mi)\\ \\x=210\ in`

`(1)/(1)(in)/(mi)=(x)/(410)(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

`(1)/(1)(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

`(1)/(1)(cm)/(km)=(x)/(337.96)(cm)/(km)\\ \\x=337.96\ cm`

`(1)/(1)(cm)/(km)=(x)/(659.83)(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

`(1)/(10)(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

`(1)/(10)(in)/(mi)=(x)/(210)(in)/(mi)\\ \\x=210/10=21\ in`

`(1)/(10)(in)/(mi)=(x)/(410)(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

`(1)/(100)(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

`(1)/(100)(ft)/(mi)=(x)/(210)(ft)/(mi)\\ \\x=210/100=2.1\ ft`

`(1)/(100)(ft)/(mi)=(x)/(410)(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

`(1)/(200)(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

`(1)/(200)(cm)/(km)=(x)/(337.96)(cm)/(km)\\ \\x=337.96/200=1.69\ cm`

`(1)/(200)(cm)/(km)=(x)/(659.83)(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

`(1)/(100)(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

`(1)/(100)(in)/(mi)=(x)/(210)(in)/(mi)\\ \\x=210/100=2.1\ in`

`(1)/(100)(in)/(mi)=(x)/(410)(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

`(1)/(1,000)(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

`(1)/(1,000)(cm)/(km)=(x)/(337.96)(cm)/(km)\\ \\x=337.96/1,000=0.34\ cm`

`(1)/(1,000)(cm)/(km)=(x)/(659.83)(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