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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 12, 4householdsearn12, 4 households earn 2, and 4 households earn $4. What is the share of total income that the top 40% earns?

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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 12each,sotheyearnatotalof1212 each, so they earn a total of 12 * 12 = $144.
  • 4 households earn 2each,sotheyearnatotalof42 each, so they earn a total of 4 * 2 = $8.
  • 4 households earn 4each,sotheyearnatotalof44 each, so they earn a total of 4 * 4 = $16.
  • Adding these amounts together, the total income is 144+144 + 8 + 16=16 = 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 * 12=12 = 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 (96/96 / 168) * 100% = 57.14%.

Therefore, the top 40% of households earn 57.14% of the total income.

This problem has been solved

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