12 households earn $12, 4 households earn $2, and 4 households earn $4. What is the share of total income that the top 40% earns?
Question
12 households earn 2, and 4 households earn $4. What is the share of total income that the top 40% earns?
Solution
To answer this question, we first need to calculate the total income and then determine the income of the top 40%.
Step 1: Calculate the total income
- 12 households earn 12 = $144.
- 4 households earn 2 = $8.
- 4 households earn 4 = $16.
- Adding these amounts together, the total income is 8 + 168.
Step 2: Determine the income of the top 40%
- There are a total of 12 + 4 + 4 = 20 households.
- The top 40% of households is 40/100 * 20 = 8 households.
- These 8 households are the 12 households that earn $12, because they have the highest income.
- So, the income of the top 40% is 8 * 96.
Step 3: Calculate the share of total income that the top 40% earns
- The share is (income of the top 40% / total income) * 100%.
- So, the share is (168) * 100% = 57.14%.
Therefore, the top 40% of households earn 57.14% of the total income.
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