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Question 1206042: An actor invests some money at 8%, and $22000 more than twice the amount at 12 %. The total annual interest earned from the investment is $30800. How much did he invest at each amount?
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
x = some amount of money invested at 8% interest rate
2x+22000 = amount invested at 12%
A = 0.08x = amount of interest earned from the 8% account
B = 0.12*(2x+22000) = interest earned from the 12% account
Each duration is for 1 year.
I'll assume simple interest is used, and not compound interest.
A+B = total interest earned for 1 year
A+B = 0.08x+0.12*(2x+22000) = 30800
Let's isolate x.
0.08x+0.12*(2x+22000) = 30800
0.08x+0.12*(2x)+0.12*(22000) = 30800
0.08x+0.24x+2640 = 30800
0.32x+2640 = 30800
0.32x = 30800-2640
0.32x = 28160
x = 28160/0.32
x = $88,000 was invested at 8%
And,
2x+22000 = 2*88000+22000 = $198,000 was invested at 12%
Check:
0.08*88000 + 0.12*198000 = 30800
The answers are confirmed.
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