Sure! I can help you practice converting measurements and proportions. Here are some example problems along with their solutions. You can try working through these, and then I'll provide explanations for each.
Problem 1: Recipe Conversion
A recipe for a cake calls for 3 cups of flour to make 12 muffins. How many cups of flour are needed to make 30 muffins?
Problem 2: Ratio of Miles to Kilometers
If 1 mile equals approximately 1.609 kilometers, how many kilometers are in 5 miles?
Problem 3: Mixing Paint
A painter mixes colors in the ratio of 2 parts red to 3 parts blue. If the painter wants to create 25 parts of paint, how many parts of red and how many parts of blue are needed?
Problem 4: Map Scale
On a map, a distance of 2 inches represents 50 miles. What distance on the map would represent 120 miles?
Problem 5: Scaling Up
A model is built to a scale of 1:50. If the height of the model is 3 feet, what is the actual height of the object it represents?
Solutions
Now, let's provide the solutions:
-
Recipe Conversion:
- The ratio of flour to muffins is \( \frac{3 \text{ cups}}{12 \text{ muffins}} \).
- To find the cups of flour for 30 muffins: \[ x \text{ cups of flour} = \frac{3}{12} \times 30 \] \[ x = \frac{3 \times 30}{12} = \frac{90}{12} = 7.5 \text{ cups of flour} \]
-
Miles to Kilometers:
- Using the conversion \(1 \text{ mile} = 1.609 \text{ kilometers}\): \[ 5 \text{ miles} \times 1.609 \text{ km/mile} = 8.045 \text{ kilometers} \]
-
Mixing Paint:
- The total parts = 2 (red) + 3 (blue) = 5 parts.
- To find the amount of red: \[ \frac{2}{5} \times 25 = 10 \text{ parts red} \]
- For blue: \[ \frac{3}{5} \times 25 = 15 \text{ parts blue} \]
-
Map Scale:
- The ratio is \( \frac{2 \text{ inches}}{50 \text{ miles}} \).
- To find the distance representing 120 miles: \[ x \text{ inches} = \frac{2}{50} \times 120 \] \[ x = \frac{2 \times 120}{50} = \frac{240}{50} = 4.8 \text{ inches} \]
-
Scaling Up:
- If the scale is 1:50, then the actual height = model height × scale factor: \[ \text{Actual height} = 3 \text{ feet} \times 50 = 150 \text{ feet} \]
Feel free to solve the problems on your own and then check your answers with the solutions provided! If you have specific measurements or proportions you want to practice with, just let me know!