Math problem college algebra?
A total of $50,000 is invested in two funds paying 8% and 10% simple interest. If the yearly interest for both funds totals $4,600, determine the amount invested at 8%.
Please help me set up the formula and help solve this please
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4600/50000 = 9.2%
10 - 9.2 = 0.8
9.2 - 8 = 1.2
The mix of investments is in reverse proportion to those distances:
12 parts of 10% to 8 parts of 8%
reduced to
3 parts of 10% to 2 parts of 8%
3 + 2 = 5 parts total
50000 / 5 = 10000 per part
3 * 10000 = 30000 ... at 10% = 3000
2 * 10000 = 20000 at 8% = . . . 1600
Total interest = . . . .. . . . . . . . 4600
Or you could do it the boring way:
x * 10% + (50000 - x) * 8% = 4600
10 x + 8 * 50000 - 8x = 460000 [ times 100 and expand the grouped terms ]
2x + 400000 = 460000
2x = 60000
x = 30000
50000 - x = 20000