Lacey made a scale drawing of the middle school. The scale of the drawing was 5 inches : 2 feet. If the gym is 170 inches wide in the drawing, how wide is the actual gym?
feet
First, we need to convert the scale ratio from inches to feet. Since 1 foot is equal to 12 inches, we can divide both sides of the ratio by 12 to convert inches to feet:
5 inches : 2 feet
(5 inches) / (12 inches/foot) : (2 feet) = 5/12 feet : 2 feet
Now we can set up a proportion to find the actual width of the gym:
(5/12 feet) / 170 inches = X feet / 1
X = (5/12 feet) * (1 / 170 inches)
X = 5/2040 feet
X = 0.00245 feet
So the actual width of the gym is approximately 0.00245 feet.
Are you sure?
Apologies for the confusion. Let's redo the calculation correctly.
The scale ratio is 5 inches : 2 feet.
To convert 170 inches to feet, we divide by 12 (since there are 12 inches in a foot):
170 inches / 12 = 14.17 feet (rounded to two decimal places)
Now, we can set up a proportion to find the actual width of the gym:
5 inches / 2 feet = 170 inches / X feet
Cross multiplying gives us:
5 inches * X feet = 2 feet * 170 inches
Simplifying, we get:
5X = 340
Dividing both sides by 5:
X = 68
Therefore, the actual width of the gym is 68 feet.
To find the actual width of the gym, we need to convert the scale from inches to feet and then use proportion to solve for the actual width.
Given:
Scale of the drawing = 5 inches : 2 feet
Width of the gym in the drawing = 170 inches
Step 1: Convert the scale from inches to feet.
Since 1 foot is equal to 12 inches, we can convert the scale as follows:
5 inches : 2 feet
Divide both sides by 12 to convert inches to feet:
5/12 inches : 2/12 feet
Simplifying this gives us:
5/12 : 1/6 feet
Step 2: Set up a proportion using the scale.
Using the proportion, we can find the actual width of the gym. Let's call the actual width "x" feet.
5/12 : 1/6 = 170 : x
Step 3: Solve for x.
We can cross-multiply and solve the proportion:
(5/12) * x = (1/6) * 170
To simplify the equation, multiply both sides by 12:
5x = 12 * (1/6) * 170
5x = 10 * 170
5x = 1700
Divide both sides by 5 to solve for x:
x = 1700 / 5
x = 340
Therefore, the actual width of the gym is 340 feet.