1.Henry built a scale model of the Washington Monument which has a height of 555 feet. In Henry’s model 1 inch represents 50 feet. What is the height of Henry’s model?
2 On a map 5 centimeters represents 20 kilometers. The distance from San Antonio to Houston is 320 kilometers. What is the distance between the two cities on the map?
A 100 cm
B 1,280 cm
C 3.2 cm
D 80 cm
555 ft * (1 in / 50 ft) = 11.1 in
feet cancel, left with inches
320 km * (5 cm / 20 km) = 80 cm
kilometers cancel, left with centimeters
To find the height of Henry's scale model, you need to set up a proportion between the actual height of the Washington Monument and the scale model's representation.
Let's define the following variables:
- Actual height of the Washington Monument: A = 555 feet
- Scale factor: S = 1 inch represents 50 feet
The proportion can be set up as follows:
A / S = X / 1
Now, substitute the known values:
555 / (1 inch/50 feet) = X / 1
Simplify the proportion:
555 * (50 feet/1 inch) = X / 1
Now, calculate the height of Henry's model:
Height of Henry's model, X = 555 * 50 = 27,750 inches
Therefore, the height of Henry's model is 27,750 inches.
To find the distance between San Antonio and Houston on the map, you will use the same concept of setting up a proportion.
Let's define the following variables:
- Distance between San Antonio and Houston on the map: X (in centimeters)
- Scale factor: S = 5 centimeters represents 20 kilometers
- Actual distance between San Antonio and Houston: A = 320 kilometers
The proportion can be set up as follows:
S / A = X / 1
Now, substitute the known values:
5 cm / 20 km = X / 1
Simplify the proportion:
5 cm / (20 km) = X / 1
Convert the units to match (convert kilometers to centimeters):
5 cm / (20 km) × (100,000 cm/1 km) = X / 1
Now, calculate the distance on the map:
X = 5 cm × (100,000 cm/1 km) × (1 km/20 km)
Simplify the calculation:
X = 5 cm × 5,000 cm = 25,000 cm
Therefore, the distance between San Antonio and Houston on the map is 25,000 cm.