proportions and scale factors practice

Answer 1

Here are some practice problems involving proportions and scale factors:

1. A map has a scale of 1 inch represents 5 miles. If two cities are 3 inches apart on the map, what is their actual distance in miles?
- Let x be the actual distance in miles.
- Set up the proportion: 1 inch / 5 miles = 3 inches / x miles.
- Cross multiply: 1*x = 3*5.
- Simplify: x = 15 miles.
- The actual distance between the cities is 15 miles.

2. An architect is designing a model building. The actual building is 30 feet tall, and the model building will be 6 inches tall. What is the scale factor of the model compared to the actual building?
- Let x be the scale factor.
- Set up the proportion: 6 inches / x = 30 feet / 1.
- Cross multiply: 6*1 = x*30.
- Simplify: 6 = 30x.
- Solve for x: x = 6/30 = 1/5.
- The scale factor of the model compared to the actual building is 1/5.

3. A recipe calls for 2 cups of flour. If you want to make half of the recipe, how much flour do you need?
- Let x be the amount of flour needed for half the recipe.
- Set up the proportion: 2 cups / 1 recipe = x cups / 1/2 recipe.
- Cross multiply: 2*(1/2) = x*1.
- Simplify: 1 = x.
- You need 1 cup of flour for half the recipe.

4. A car traveled 100 miles in 2 hours. If the car continues to travel at the same rate, how far will it go in 5 hours?
- Let x be the distance traveled in 5 hours.
- Set up the proportion: 100 miles / 2 hours = x miles / 5 hours.
- Cross multiply: 100*5 = 2*x.
- Simplify: 500 = 2x.
- Solve for x: x = 500/2 = 250 miles.
- The car will travel 250 miles in 5 hours.

These are just a few examples of proportions and scale factor problems. Remember to set up the proportions correctly and solve for the unknown variable to find the desired answer.