Final answer:
Emma has $282 in the 12% savings account and $1232 in the 13% savings account. The problem is solved by setting up a system of linear equations based on the given interest rates and total interest earned.
Step-by-step explanation:
To solve the problem involving Emma's savings accounts with different interest rates, we'll use a system of linear equations. Emma has two bank accounts, one with an interest rate of 12% and the other with an interest rate of 13%. If she has $950 more in the 13% account than the 12% account, and the total interest from both accounts is $194, we need to determine the amount invested in each account.
Let's denote the amount in the 12% account as x and the amount in the 13% account as x + $950. The total interest (I) earned is $194. We can now express the total interest earned from each account as follows:
- Interest from 12% account: 0.12x
- Interest from 13% account: 0.13(x + $950)
The equation that represents the total interest from both accounts is:
0.12x + 0.13(x + $950) = $194
This simplifies to:
0.12x + 0.13x + $123.5 = $194
Combining like terms, we get:
0.25x = $70.5
Dividing both sides by 0.25:
x = $282
Therefore, Emma has $282 in the 12% account and $1232 (282 + $950) in the 13% account.