Bill invested a total of $\$ 28,000$ in three different mutual funds. After one year, the first fund had shown a loss of 5\%, the second had shown a profit of $9 \%$, and the third fund had shown a profit of $13 \%$. In the first year Bill made a profit of $\$ 2600$ from the three funds. If Bill invested $\$ 4000$ more in the fund that made a profit of $9 \%$ than he did in the fund that lost $5 \%$, how much did he initially invest in each fund?
A) $\$ 8000$ at a loss of $5 \%, \$ 4000$ at a profit of $9 \%, \$ 16,000$ at a profit of $13 \%$
B) $\$ 4000$ at a loss of $5 \%, \$ 8000$ at a profit of $9 \%, \$ 16,000$ at a profit of $13 \%$
C) $\$ 3000$ at a loss of $5 \%, \$ 7000$ at a profit of $9 \%, \$ 18,000$ at a profit of $13 \%$
D) $\$ 5000$ at a loss of $5 \%, \$ 9000$ at a profit of $9 \%, \$ 14,000$ at a profit of $13 \%$

Question

Quizplus · Accepted Answer

Bill invested \$4000 more in the 9% fund than the 5% fund. Let x be the amount in the 5% fund, then x + 4000 is in the 9% fund. The rest, 28000 - x - (x + 4000) = 24000 - 2x, is in the 13% fund. The equation for profit is: -0.05x + 0.09(x + 4000) + 0.13(24000 - 2x) = 2600. Solving gives x = 4000, so he invested \$4000 at 5%, \$8000 at 9%, and \$16000 at 13%.

Bill Invested a Total Of $28,000\$ 28,000$28,000 In Three Different Mutual Funds

Bill Invested a Total Of $\$ 28,000$ In Three Different Mutual Funds