Applying Proportion to Scale Models

Solve for x

• x=6

• x =1/6

• x = 7

• x=9

Answer explanation

To solve for x, we can set up the equation based on the problem context. After simplifying, we find that x = 6 is the solution that satisfies the equation, making it the correct choice.

The pair of figures is similar. Find the missing side.

• x = 20

• x = 12

• x = 5

• x = 4

Answer explanation

Since the figures are similar, the ratios of corresponding sides are equal. By setting up the proportion and solving for x, we find that x = 5 is the correct answer, matching the ratio of the known sides.

Using 2 in = 35 miles, solve:  The distance between Troy City and Ben City is 315 miles. How far apart are they on the map?

• 18 miles

• 18 inches

• 5512.5 inches

• 5512.5 miles

Answer explanation

To find the map distance, use the ratio: 2 inches = 35 miles. For 315 miles, set up the proportion: (2 inches / 35 miles) = (x inches / 315 miles). Solving gives x = 18 inches, so they are 18 inches apart on the map.

A model of a car has a scale of 3 cm: 2 m. The length of the actual hood of the car is 1 m. What is the length of the hood of the model?

• 1.5 m

• 1.5 cm

• 15 cm

• 6 cm

Answer explanation

The scale 3 cm: 2 m means 3 cm on the model represents 2 m in reality. To find the model hood length for a 1 m actual hood, set up a proportion: (3 cm / 2 m) = (x cm / 1 m). Solving gives x = 1.5 cm.

Scale: 1in.=7ft. The actual width of the backyard is 49 ft, how wide is it in the drawing?

• 14 in 

• 7 in

• 42 in

• 56 in

Answer explanation

To convert the actual width of 49 ft to the drawing, use the scale 1 in = 7 ft. Divide 49 ft by 7 ft/in: 49 ÷ 7 = 7 in. Thus, the width in the drawing is 7 in.

From Denver to Chicago = 3 in. If the scale is 1 in = 300 miles, find the actual distance.

• 300 miles

• 1000 miles

• 900 miles

• 600 miles

Answer explanation

To find the actual distance, multiply the scale distance by the scale factor: 3 in. x 300 miles/in. = 900 miles. Therefore, the actual distance from Denver to Chicago is 900 miles.

A flagpole is 1 in.= 4 ft. If the pole measures 12 inches, how tall is the actual pole?

• 16 feet

• 3 feet

• 48 feet

• 9 feet

Answer explanation

The flagpole ratio is 1 in. = 4 ft. If the pole is 12 inches, then 12 in. x 4 ft/in. = 48 ft. Therefore, the actual height of the pole is 48 feet.

A model of a planned baseball stadium is 2 ft wide. The actual stadium will be 200 yd wide. What is the scale?

• 2 feet = 50 yards

• 1 foot = 200 yards

• 1 foot = 100 yards

• 1 foot = 50 yards

Answer explanation

To find the scale, convert 200 yards to feet (200 yd = 600 ft). The model is 2 ft wide, so the scale is 2 ft : 600 ft, which simplifies to 1 ft : 300 ft. Thus, 1 ft = 100 yards is the correct scale.

On a map, the distance between two towns in 2.6 cm. The scale of the map is 1 cm:50 km. What is the actual distance between the two towns?

• 100 km

• 130 km

• 70 km

• 150 km

Answer explanation

To find the actual distance, multiply the map distance by the scale: 2.6 cm x 50 km/cm = 130 km. Thus, the actual distance between the two towns is 130 km.

What is the scale factor?

• 4

• .25

• 5

• 6

Answer explanation

The scale factor is the ratio of the dimensions of a model to the actual dimensions. In this case, the correct scale factor is 4, meaning the model is 4 times larger than the actual size.