Inga invested part of her $6000 savings in common stock and the rest in rare stamps. At the end of the year, she realized a gain of 9% on the stock and 12% on the stamps. If her savings now amounts to $6615, how much did she invest in stamps?
Let x be the amount Inga invested in rare stamps.
Inga earned a 9% gain on the stock, so she earned 6000 * 9% = $<<6000*9*.01=540>>540 from the stock.
Inga earned a 12% gain on the stamps, so she earned x * 12% = 0.12x from the stamps.
In total, Inga earned 540 + 0.12x = $6615.
Thus, the total amount Inga invested in stamps is x = $<<6615-540=6075>>6075. Answer: \boxed{6075}.
Let's assume Inga invested $x in common stock. Since she invested the rest in rare stamps, she invested $6000 - $x in stamps.
Based on the information given, Inga realized a gain of 9% on the stock and 12% on the stamps. We can calculate the total gain from both investments:
Total gain = (9/100) * x + (12/100) * (6000 - x)
According to the question, Inga's savings now amount to $6615, so we can set up the following equation:
$6615 - $6000 = Total gain
Simplifying further:
$615 = (9/100) * x + (12/100) * (6000 - x)
Multiplying both sides by 100 to remove the denominators:
61500 = 9x + 12(6000 - x)
61500 = 9x + 72000 - 12x
Combining like terms:
-10500 = -3x
Dividing both sides by -3:
x = 3500
So Inga invested $3500 in common stock. To find out how much she invested in stamps, we subtract this amount from her total savings:
$6000 - $3500 = $2500
Therefore, Inga invested $2500 in stamps.