a). The length of the classroom is 30 ft. The length of the room on the scale drawing is 6 in. Is this correct? Explain why or why not.

Michael has made a scale drawing of his classroom. The scale for his drawing is 0.5 in. : 3 ft.
b). One of the student tables is 6 ft long. How long should it be on the drawing? Explain how you got your answer
c.)Write your own problem concerning Michael’s drawing. Solve and explain your answers.

a. Scale = 30Ft/6in = 5 Ft/in. 0r 1in =

5 Ft.

a) To determine if the length of the classroom on the scale drawing is correct, we can use the scale ratio.

The scale for the drawing is given as 0.5 in. : 3 ft. This means that every 0.5 inches on the drawing represents 3 feet in reality.

If the length of the classroom is 30 ft, we can find the length on the scale drawing by setting up a proportion:

1 inch (on the drawing) / x inches (on the drawing) = 3 ft (in reality) / 30 ft (in reality)

Simplifying the proportion, we get:
1/x = 3/30
1/x = 1/10

Cross-multiplying, we find:
x = 10

Therefore, the length of the classroom on the scale drawing should be 10 inches, not 6 inches. The statement is incorrect because the length is shorter on the scale drawing than in reality.

b) To determine the length of the student table on the drawing, we can use the same scale ratio of 0.5 in. : 3 ft.

If the length of the student table is 6 ft, we can set up a proportion:
0.5 in (on the drawing) / x inches (on the drawing) = 3 ft (in reality) / 6 ft (in reality)

Simplifying the proportion, we get:
0.5/x = 3/6
0.5/x = 1/2

Cross-multiplying, we find:
x = 1

Therefore, the length of the student table on the scale drawing should be 1 inch.

c) Problem: Michael's scale drawing for his classroom shows a bookshelf that is 5 inches long. If the actual length of the bookshelf is 10 feet, determine the scale ratio used in Michael's drawing.

Solution:
Using the ratio 5 inches (on the drawing) / x inches (on the drawing) = 10 ft (in reality) / x ft (in reality), we can find the scale ratio.

Simplifying the proportion, we get:
5/x = 10/x

Cross-multiplying, we find:
5x = 10

Dividing both sides by 5, we get:
x = 2

Therefore, the scale ratio used in Michael's drawing is 2 inches : 10 feet.

a) To determine if the length of the classroom on the scale drawing is correct, we need to compare the ratio of the actual length to the length on the scale drawing.

First, convert the length of the classroom from feet to inches. Since there are 12 inches in a foot, multiply the length of the classroom by 12:
30 ft * 12 in/ft = 360 in

Next, compare this to the length on the scale drawing, which is 6 inches. The ratio of the actual length to the length on the scale drawing should be the same as the ratio given by the scale.

Given scale: 0.5 in. : 3 ft

To find the corresponding length on the scale drawing, we can set up a proportion:
0.5 in / 3 ft = x in / 360 in

To solve for x, we cross-multiply:
(0.5)(360) = 3x
180 = 3x
x = 60

The length on the scale drawing should be 60 inches, not 6 inches. Therefore, the length of the classroom on the scale drawing is not correct.

b) To determine the length of the student table on the scale drawing, we can use the given scale: 0.5 in. : 3 ft

Since the actual length of the student table is 6 ft, we need to find the corresponding length on the scale drawing.

Set up a proportion:
0.5 in / 3 ft = x in / 6 ft

To solve for x, we cross-multiply:
(0.5)(6) = 3x
3 = 3x
x = 1

Therefore, the student table should be 1 inch long on the drawing.

c) Problem: Michael's scale drawing has a scale of 0.25 in. : 2 ft. What would be the length of a bookshelf that is 8 ft long on the scale drawing? Explain how you got your answer.

To find the length of the bookshelf on the scale drawing, we can use the given scale: 0.25 in. : 2 ft

Since the actual length of the bookshelf is 8 ft, we need to find the corresponding length on the scale drawing.

Set up a proportion:
0.25 in / 2 ft = x in / 8 ft

To solve for x, we cross-multiply:
(0.25)(8) = 2x
2 = 2x
x = 1

Therefore, the bookshelf would be 1 inch long on the scale drawing.

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