Sam invested a total if $29,000 in two accounts paying 8% and 5% annual interest, respectively. How much was invested in each account if, after one year, the total interest was $1,795.00
Let x be the amount invested at 8% annual interest.
Then the amount invested at 5% annual interest is $29,000 - x.
The interest from the amount invested at 8% annual interest is x * 8/100 = 0.08x.
The interest from the amount invested at 5% annual interest is (29,000 - x) * 5/100 = 0.05(29,000 - x).
The total interest is the sum of the interest from both accounts, so 0.08x + 0.05(29,000 - x) = $1,795.00.
Expanding the equation gives 0.08x + 0.05*29,000 - 0.05x = $1,795.00.
Combining like terms gives 0.03x + 0.05*29,000 = $1,795.00.
Subtracting 0.05*29,000 from both sides of the equation gives 0.03x = $1,795.00 - 0.05*29,000.
Combining like terms gives 0.03x = $1,795.00 - $1,450.00.
Subtracting $1,450.00 from both sides of the equation gives 0.03x = $345.00.
Dividing both sides of the equation by 0.03 gives x = $345.00 / 0.03.
Dividing gives x = $11,500.00.
The amount invested at 8% annual interest is $11,500.00.
The amount invested at 5% annual interest is $29,000 - $11,500.00 = $17,500.00. Answer: \boxed{11,500, 17,500}.
Let's assume the amount invested in the account that pays 8% annual interest is x dollars.
Since the total amount invested is $29,000, the amount invested in the account that pays 5% annual interest would be (29000 - x) dollars.
The interest earned from the account that pays 8% annual interest would be 0.08x dollars.
The interest earned from the account that pays 5% annual interest would be 0.05(29000 - x) dollars.
According to the information given, the total interest earned after one year is $1,795.00.
So, we can set up the equation:
0.08x + 0.05(29000 - x) = 1795
Now, let's solve this equation step by step:
0.08x + 0.05 * (29000 - x) = 1795
0.08x + 1450 - 0.05x = 1795
0.08x - 0.05x = 1795 - 1450
0.03x = 345
x = 345 / 0.03
x ≈ 11,500
So, Sam invested approximately $11,500 in the account that pays 8% annual interest.
The amount invested in the account that pays 5% annual interest would be 29000 - 11,500 = $17,500.
Therefore, Sam invested $11,500 in the account that pays 8% annual interest and $17,500 in the account that pays 5% annual interest.