You receive a total of 1,350 a year in interest from three investments. The interest rates for the three investments are $5 \% , 6.5 \%$ and 7.5% . The 6.5% investment is half of the 5% investment, and the 7.5% investment is 3000 less than the 5% investment. What is the amount of the $6.5 \%$ investment?
A) $\$ 5,000$
B) $\$ 6,000$
C) $\$ 10,000$
D) $\$ 7,000$
E) $\$ 3,000$

Question

You receive a total of 1,350 a year in interest from three investments. The interest rates for the three investments are $5 \% , 6.5 \%$ and 7.5% . The 6.5% investment is half of the 5% investment, and the 7.5% investment is 3000  less than the 5% investment. What is the amount of the $6.5 \%$ investment?
A) $\$ 5,000$
B) $\$ 6,000$
C) $\$ 10,000$
D) $\$ 7,000$
E) $\$ 3,000$

Quizplus · Accepted Answer

Let the amount of the 5% investment be $x$, the 6.5% investment be $y$, and the 7.5% investment be $z$. From the information given, we have $y = \frac{1}{2}x$ and $z = x - 3000$. The total interest from all investments is $1350 = 0.05x + 0.065y + 0.075z$. Substituting $y$ and $z$ in terms of $x$ into the equation and solving for $x$, we can find the value of $y$. The correct answer is $y = \$5,000$, which matches the conditions given.

You Receive a Total of 1,350 a Year in Interest 5%,6.5%5 \% , 6.5 \%5%,6.5%

You Receive a Total of 1,350 a Year in Interest $5 \% , 6.5 \%$