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Algebra Problem

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The butcher, the baker, and the candlestick maker purchased a lottery ticket together and won $36,000 in the weekly lottery drawing. Since the three friends each have different risk tolerances and investment strategies, they decided that each of them would receive a certain amount of money to invest for the future.

The butcher chose to invest in a low-risk investment that is projected to pay 6% simple interest.
The baker invested his money in a medium-risk investment projected to pay 8% simple interest.
The candlestick maker invests his money in a higher-risk investment that is projected to pay 10% simple interest.

Since the baker chose the numbers, the men decide that he should receive $4000 less than the sum of what the other two men receive together. If the total annual interest from all three investments is projected to be $2,880, how much is invested in each fund? Check your solution.

x = amount invested at 6%
y= amount invested at 8%
z = amount invested at 10%

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