A map maker has created a new map of North America. The map has a length of 30 inches and a width of 24 inches and a scale of 1 inch = 200 miles. After creating the map, he sent it to the printing company. The printing company plans to make several scaled versions of the map. Since each size will have its own scale, they made a mock-up of each version and sent them to the map maker to get his final approval before they start printing.

Match the correct map dimensions to its correct scale, if shown.

1 inch = 300 miles

1 inch = 50 miles

1 inch = 600 miles

1 inch = 100 miles

scale not shown

1 inch = 400 miles

Map 1:

width of 12 inches

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Map 2:

length of 20 inches

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Map 3:

area of 80 square inches

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Map 4:

width of 4 inches

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Map 5:

length of 60 inches

Map 1:

Width of 12 inches → 1 inch = 400 miles ⇒ 6th

Map 2:

Length of 20 inches → 1 inch = 300 miles ⇒ 1st

Map 3:

Area of 80 inches → 1 inch = 600 miles ⇒ 3rd

Map 4:

Scale not shown ⇒ 5th

Map 5:

Length of 60 inches → 1 inch = 100 miles ⇒ 4th

Step-by-step explanation:

The map scale is:

1 inch = 200 miles

The dimensions of the map are:

length of 30 inches and width of 24 inches

→ 1 : 200

→ 24 : x

→ 30 : y

By using cross multiplication

∴ x = 4800 ⇒ actual width

∴ y = 6000 ⇒ actual length

Let us take the dimension in each map to find its scale

Map 1:

∵ Width of 12 inches

→ 1 : m

→ 12 : 4800

By using cross multiplication

∴ 12 m = 4800

- Divide both sides by 12

∴ m = 400

∴ The scale of the map is 1 : 400

Map 1:

Width of 12 inches → 1 inch = 400 miles

Map 2:

∵ length of 20 inches

→ 1 : n

→ 20 : 6000

By using cross multiplication

∴ 20 n = 6000

- Divide both sides by 20

∴ n = 300

∴ The scale of the map is 1 : 300

Map 2:

Length of 20 inches → 1 inch = 300 miles

Map 3:

∵ Area of 80 inches²

∵ Area of the original map = 24 * 30 = 720 inches²

→ (1 inch) ² : (1 mile) ²

→ 1² : 200²

→ 720 : q

By using cross multiplication

∴ q = 28800000

Let us find the scale

→ 1² : p²

→ 80 : 28800000

By using cross multiplication

∴ 80 p² = 28800000

- Divide both sides by 80

∴ p² = 360000

- Take √ for both sides

∴ P = 600

∴ The scale of the map is 1 : 600

Map 3:

Area of 80 inches → 1 inch = 600 miles

Map 4:

∵ Width of 4 inches

→ 1 : f

→ 4 : 4800

By using cross multiplication

∴ 4 f = 4800

- Divide both sides by 4

∴ f = 1200

∴ The scale of the map is 1 : 1200

Map 4:

Width of 4 inches → 1 inch = 1200 miles ⇒ scale not shown

Map 5:

∵ length of 60 inches

→ 1 : g

→ 60 : 6000

By using cross multiplication

∴ 60 g = 6000

- Divide both sides by 60

∴ g = 100

∴ The scale of the map is 1 : 100

Map 5:

Length of 60 inches → 1 inch = 100 miles