This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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To prepare a pie diagram, we need to calculate the total expenditure for each family and then determine the angle for each item's sector in the circle. A full circle represents 360^. For Family A Step 1: Calculate the total expenditure for Family A. Total Expenditure (Family A) = 1700 + 800 + 400 + 400 + 200 + 100 = 3600 Step 2: Calculate the angle for each item for Family A. The formula for the angle of a sector is: Angle = ( Expenditure for itemTotal Expenditure ) × 360^ • Food: (1700)/(3600) × 360^ = 170^ • Clothes: (800)/(3600) × 360^ = 80^ • Fuel: (400)/(3600) × 360^ = 40^ • Rent: (400)/(3600) × 360^ = 40^ • Education: (200)/(3600) × 360^ = 20^ • Miscellaneous: (100)/(3600) × 360^ = 10^ Step 3: Summarize the angles for Family A. | Item | Expenditure | Angle (in degrees) | | :------------ | :---------- | :----------------- | | Food | 1700 | 170^ | | Clothes | 800 | 80^ | | Fuel | 400 | 40^ | | Rent | 400 | 40^ | | Education | 200 | 20^ | | Miscellaneous | 100 | 10^ | | Total | 3600 | 360^ | For Family B Step 1: Calculate the total expenditure for Family B. Total Expenditure (Family B) = 3300 + 900 + 800 + 600 + 600 + 200 = 6400 Step 2: Calculate the angle for each item for Family B. • Food: (3300)/(6400) × 360^ = 185.625^ • Clothes: (900)/(6400) × 360^ = 50.625^ • Fuel: (800)/(6400) × 360^ = 45^ • Rent: (600)/(6400) × 360^ = 33.75^ • Education: (600)/(6400) × 360^ = 33.75^ • Miscellaneous: (200)/(6400) × 360^ = 11.25^ Step 3: Summarize the angles for Family B. | Item | Expenditure | Angle (in degrees) | | :------------ | :---------- | :----------------- | | Food | 3300 | 185.625^ | | Clothes | 900 | 50.625^ | | Fuel | 800 | 45^ | | Rent | 600 | 33.75^ | | Education | 600 | 33.75^ | | Miscellaneous | 200 | 11.25^ | | Total | 6400 | 360^ | How to prepare the pie diagrams: 1. Draw a circle for Family A and another circle for Family B. 2. Mark the center of each circle. 3. Draw a radius from the center to the circumference. This will be the starting line for the first sector. 4. Using a protractor, measure and draw the angle for each item, starting from the previous line. For example, for Family A, draw a 170^ sector for Food, then from the end of that sector, draw an 80^ sector for Clothes, and so on. 5. Label each sector with its corresponding item (e.g., Food, Clothes) and its percentage or value. 6. Optionally, use different colors or patterns for each sector to distinguish them. The calculated angles for each family are: Family A: Food: 170^ Clothes: 80^ Fuel: 40^ Rent: 40^ Education: 20^ Miscellaneous: 10^ Family B: Food: 185.625^ Clothes: 50.625^ Fuel: 45^ Rent: 33.75^ Education: 33.75^ Miscellaneous: 11.25^