Final answer:
Miguel invested $16,000 in Fund B.
Step-by-step explanation:
To find out how much Miguel invested in Fund B, we can set up a system of equations using the information given. Let x represent the amount Miguel invested in Fund B.
From the first sentence, it is given that the amount Miguel invested in Fund A is $16,000. This returned a 10% profit, so the profit from Fund A is 0.1 * $16,000 = $1,600.
The total amount Miguel invested in both funds is $16,000 + x, and the total profit from both funds is 7% of that amount. So, the total profit is 0.07 * ($16,000 + x).
Since the total profit is the sum of the profits from Fund A and Fund B, we have the equation:
$1,600 + 0.07 * ($16,000 + x) = 0.07 * ($16,000)
Simplifying this equation gives:
$1,600 + 0.07x + 0.07 * $16,000 = 0.07 * $16,000
Combining like terms and solving for x:
0.07x = 0.07 * $16,000 - $1,600
0.07x = $1,120
x = $1,120 / 0.07
x = $16,000
Therefore, Miguel invested $16,000 in Fund B.