Final answer:
None of the given options accurately reflect the correct amounts in each account. After setting up a system of equations and solving it, Francisco invested $5,100 in the first account at 14% interest and $3,800 in the second account at 12% interest to earn a total of $1,170 in one year.
Step-by-step explanation:
To determine how much was invested in each account, we can set up a system of equations. We know that the total investment is $8,900 and the total interest earned is $1,170 at the end of one year. We can let x be the amount invested in the first account at 14% interest, and y be the amount in the second account at 12% interest.
The system of equations based on the information given would be:
- x + y = 8,900 (Total investment)
- 0.14x + 0.12y = 1,170 (Total interest)
Now, we can solve this system using substitution or elimination. Let's use substitution:
From the first equation, we can express y in terms of x: y = 8,900 - x. Now substitute y in the second equation:
0.14x + 0.12(8,900 - x) = 1,170
Simplifying this, we get:
0.14x + 1,068 - 0.12x = 1,170
Now, combine like terms and solve for x:
0.02x = 102
x = 5,100
Now, we can find y using the expression y = 8,900 - x:
y = 8,900 - 5,100
y = 3,800
Therefore, the correct answer is $5,100 in the first account and $3,800 in the second account, which means that none of the given options (A, B, C, D) are correct.