Final answer:
Ms. Suzuki invested $9,000 at 8% and $5,000 at 10%. This was determined by setting up a system of equations based on the total amount invested and the total interest earned, then solving for the amounts in each account.
Step-by-step explanation:
Ms. Suzuki invested $14,000 in two different interest-bearing accounts, one at 8% annual interest and the other at 10% annual interest. She received a total of $1,220 in interest at the end of the year. To determine how much she invested in each account, we can set up a system of equations:
- Let x be the amount invested at 8%.
- Let y be the amount invested at 10%.
The total amount invested is $14,000, which leads to our first equation: x + y = 14,000
The total interest from both accounts is $1,220, leading to our second equation based on the interest rates: 0.08x + 0.10y = 1,220
Solving these simultaneous equations, we start by multiplying the second equation by 100 to clear the decimals: 8x + 10y = 122,000
Next, we can multiply the first equation by 8 to help eliminate a variable: 8x + 8y = 112,000
Subtracting the fourth equation from the third gives us: 2y = 10,000
Dividing through by 2, we find that y = $5,000. Substituting y into the first equation x + 5,000 = 14,000 gives us x = $9,000.
Thus, Ms. Suzuki invested $9,000 at 8% and $5,000 at 10%.
Answer choice (d) is correct.