SOLUTION: Yet another brain cramp! I figured out the answer, but the exact equation to get there escapes me. A man invests $6,000 at a certain rate and $8,000 at a rate that is 1% less than

Question 32387: Yet another brain cramp! I figured out the answer, but the exact equation to get there escapes me. A man invests $6,000 at a certain rate and $8,000 at a rate that is 1% less than twice the rate at $6,000. If the total income from both investments is $1,240, find the rate of each investment. I got 6 % and 11% respectively, but I guessed, checked and revised. My daughter needs an equation. Thanks in advance.
Answer by mukhopadhyay(490) (Show Source): You can put this solution on YOUR website!
Assume that the person invests $6,000 at x% rate.
$8,000 is then invested at (2x-1)%
Total interest = x% of 6000 + (2x-1)% of 8000
=(x/100)(6000) + [(2x-1)/100](8000)
=60x + 80(2x-1)
=60x + 160x - 80
=220x - 80
Total earnings from the interest = 1240
=> 220x - 80 = 1240
=> 220x = 1320
=> x = 6
So, $6,000 invested at 6% and $8,000 invested at 11%

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