Confusing money word problem

[bluesocks11]

Find the weighted average tax paid by this 50% of taxpayers.

5% of taxpayers paid an average of $86,000, another 5% paid an average of $18,000, another 15% paid an average of $9,000, and another 25% paid an average of $3,500. Find the weight aveage tax paid by 50% of these taxpayers.


My work:

86,000 + 18,000 + 9,000 + 3,500 = 116,500/4 = $29,125 by paid 50% of the people.

is that what the average means? Just adding the money and averaging it by how many people there are.

 

[Ishuda]

Find the weighted average tax paid by this 50% of taxpayers.

5% of taxpayers paid an average of $86,000, another 5% paid an average of $18,000, another 15% paid an average of $9,000, and another 25% paid an average of $3,500. Find the weight aveage tax paid by 50% of these taxpayers.


My work:

86,000 + 18,000 + 9,000 + 3,500 = 116,500/4 = $29,125 by paid 50% of the people.

is that what the average means? Just adding the money and averaging it by how many people there are.

Not quite the way you have done it. Just to work a concrete example, suppose there were 100 people. Then
5 people paid an average of $86K or 5 * 86K = 430K
5 people paid an average of $18K or 5 * 18 = $90K
15 people paid an average of $9K or 15 * 9 = $135K
25 people paid an average of $3.5K or 25 * 3.5 = $87.5K
or
50 people paid a total of ...

From this we can see what is meant by the weighted average. The weights are the number of people, so you multiply each value by the value of the weight. To get the average, you divide by the number of people which is just the sum of the weights. For the actual problem the weights are percentages; 0.05, 0.05, 0.15, 0.25 and you divide by the sum of the weights or by 0.50 which is 50%. Notice that the actual number of people 'cancels out' as it should and we are just left with a percentage again.