Banking math question help!?

The annual interest on Sid Carrington's three investments amounted to $38500: 5% on a savings account, 9% on mutual funds, and 12% on bonds. If the amount of Sid's investment in bonds was triple the amount of his investment in the savings account, and the interest earned from his investment in bonds was equal to the dividends he received from his investment in mutual funds, find how much money he placed in each type of investment

savings = $83,695
bonds = $251,085
mutual funds = $46,497

Set savings =s, bonds = b, and mutual funds = m. Now create formulas using the information given:
b=3s
.05s + .09m + .12b = $38,500
.05s = .09m

Now, solve for s by replacing the variables in the second formula, with variables from the first and third formulas:
so, the second formula becomes:
.05s + .05s + (.12)(3s) = 38,500
solve for s, and you get s = 83,695
now, substitue 83,695 for s in the other 2 equations, and solve for m and b.

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