Question

The Hayes family has invested $10,000. Part of the money is invested at a 5% rate of return, and the remainder at 7%. If the total income from these investments is $540, how much is invested at each rate? (Income from an investment is the product of the rate of return and the amount invested.)

a. $3,000 at 5%, $7,000 at 7%
b. $4,000 at 5%, $6,000 at 7%
c. $5,000 at 5%, $5,000 at 7%
d. $6,000 at 5%, $4,000 at 7%

Answer 1

After setting up and solving the equation based on the total investment and the income from both rates, we find that the Hayes family invested $8,000 at 5% and $2,000 at 7% to achieve the total income of $540 from their investments.

Step-by-step explanation:

The question asks us to determine how much the Hayes family invested at each interest rate given that part of their $10,000 investment was at a 5% rate and the remainder at a 7% rate, with total income from these investments being $540.

Let's denote the amount invested at 5% as x, and thus the amount invested at 7% would be $10,000 - x. The income from the investment at 5% would then be 0.05x, and the income from the 7% would be 0.07($10,000 - x).

The total income from both investments is $540, which gives us the equation:
0.05x + 0.07($10,000 - x) = $540. Solving this equation for x, we get:
0.05x + $700 - 0.07x = $540,
-0.02x = $540 - $700,
-0.02x = -$160,
x = $8,000.

Therefore, $8,000 is invested at 5%, and the remainder, $2,000, is invested at 7%.