Question

A portion of $7200 is invested at a 4% annual return, while the remainder is invested at a 5% annual return. If the annual income from both portions is the same, what is the total income from the two investments?

a) $288
b) $360
c) $400
d) $432

Answer 1

Upon solving the equations, we find that the annual income from each investment is $160, leading to a total income of $320. However, this result is not listed in the answer choices, suggesting there may be an error in the question or the calculations.

Step-by-step explanation:

To solve this problem, we'll let the portion of the $7200 that is invested at 4% annual return be 'x'. Therefore, the remaining amount, which will be $7200 - x, is invested at a 5% annual return. Since the annual income from both portions is the same, the equations for the income from each investment can be set equal to each other.

4% of 'x' equals 5% of ($7200 - x):
0.04x = 0.05($7200 - x)

Solving for 'x' gives us:
0.04x = 0.05 × 7200 - 0.05x
0.04x + 0.05x = 0.05 × 7200
0.09x = 360
x = $4000

Therefore, $4000 is invested at 4% and $3200 ($7200 - $4000) at 5%. The annual income from each investment is 4% of $4000 which is $160, and likewise, 5% of $3200 is also $160. So, the total income from the two investments is 2 × $160 = $320, but this option is not listed. It seems there is a discrepancy here, so we need to check our calculations or possibly the question itself to ensure we have not made a mistake or misinterpreted the information.