Question

Fran invested $700 in two funds that pay 6% and 5.5% annual interest. Fran's combined annual interest is $40.50. How much of the $700 was invested in each fund?

a) $400 in the 6% fund and $300 in the 5.5% fund
b) $300 in the 6% fund and $400 in the 5.5% fund
c) $350 in the 6% fund and $350 in the 5.5% fund
d) $320 in the 6% fund and $380 in the 5.5% fund

Answer 1

By setting up a system of equations based on the total investment and the annual interest from each fund, we determine that $400 was invested at 6% and $300 was invested at 5.5%.

Step-by-step explanation:

The question involves an algebraic word problem where Fran invested a total of $700 in two separate funds, earning different annual interest rates. One fund pays 6% interest while the other pays 5.5% interest, and the total interest earned from both investments is $40.50. We can set up a system of equations to solve for the amount invested in each fund.

Let x represent the amount invested at 6%, and let y represent the amount invested at 5.5%. We have two equations from the problem statement:

• The total amount invested is $700: x + y = 700
• The total interest earned is $40.50, which is equal to the sum of the interest from both investments: 0.06x + 0.055y = 40.50

By solving this system of equations, we find that $400 was invested in the 6% fund and $300 was invested in the 5.5% fund, which corresponds to option (a). The mathematics behind solving the system involves substitution or elimination method.