Final answer:
To determine how much Sally has in each of her two accounts, we set up a system of equations using the total investment amount and the difference in interest earned. Solving this system, we find that Sally has $3,400 in the 6% mutual fund and $5,500 in the 2% CD account.
Step-by-step explanation:
To solve the mathematical problem completely where Sally has $8,900 invested in two accounts, with one account being a 6% mutual fund and the other a 2% CD (Certificate of Deposit), we can set up a system of equations to determine how much she has in each account.
Let x represent the amount of money in the 6% mutual fund, and y represent the amount in the 2% CD. The total amount of money invested is $8,900, so we have our first equation:
x + y = 8,900
According to the problem, Sally earns $182 more in interest from the mutual fund than she does from the CD. Since interest is a percentage of the principal (the amount invested), we can express the interest earned from each account:
Interest from the mutual fund is 0.06x and from the CD is 0.02y. The mutual fund earns $182 more than the CD, leading to our second equation:
0.06x = 0.02y + 182
Now we have a system of equations:
- x + y = 8,900
- 0.06x = 0.02y + 182
We will solve the second equation for x:
x = (0.02y + 182) / 0.06
Substitute the expression for x into the first equation:
((0.02y + 182) / 0.06) + y = 8,900
After solving for y, we find that y = $5,500. Then we can find x by subtracting y from the total amount invested:
x = 8,900 - 5,500 = $3,400
Therefore, Sally has $3,400 in the 6% mutual fund and $5,500 in the 2% CD.