A total of $4,000 was invested, part of it at 6% interest and the remainder at 8%. If the total yearly interest amount is $260, how much was invested at 6%
6% investment --- x
8% investment = 4000-x
.06x + .08(4000-x) = 260
times 100
6x + 8(4000-x) = 26000
solve for x
Well, well, well! Looks like we have a financial detective on our hands. Let me put my clown hat on and do some math magic for you!
Let's assume that the amount invested at 6% interest is "X" (don't worry, it's not related to the X-Men).
So, the amount invested at 8% interest would be the remainder, which is $4,000 - X. You following me?
Now, we need to calculate the interest earned on each investment.
Interest from the 6% investment would be X multiplied by 6/100 (or 0.06), which is 0.06X.
The interest from the 8% investment would be ($4,000 - X) multiplied by 8/100 (or 0.08), which is 0.08(4,000 - X).
Since the total yearly interest is $260, we can set up an equation:
0.06X + 0.08(4,000 - X) = 260
Now, it's time for some serious math clowning around. Are you ready?
0.06X + 0.08(4,000) - 0.08X = 260
0.06X + 320 - 0.08X = 260
-0.02X + 320 = 260
Subtract 320 from both sides:
-0.02X = -60
Divide by -0.02:
X = 3,000
So, $3,000 was invested at a 6% interest rate. Ta-dah!
To determine how much was invested at 6% interest, let's use algebraic equations.
Let x represent the amount invested at 6% interest.
Since the total investment is $4,000, the amount invested at 8% interest can be expressed as (4,000 - x).
The yearly interest earned from the amount invested at 6% interest is calculated as (x * 0.06).
The yearly interest earned from the amount invested at 8% interest is calculated as ((4,000 - x) * 0.08).
According to the problem, the total yearly interest amount is $260, so we can construct the equation:
(x * 0.06) + ((4,000 - x) * 0.08) = 260
Now, let's solve the equation step by step:
0.06x + 0.08(4,000 - x) = 260
0.06x + 320 - 0.08x = 260
-0.02x = 260 - 320
-0.02x = -60
x = (-60) / (-0.02)
x = 3,000
Therefore, $3,000 was invested at 6% interest.
To find the amount invested at 6%, we can set up a system of equations based on the given information.
Let's assume that the amount invested at 6% is x dollars. Since the total amount invested is $4,000, the amount invested at 8% can be represented as (4000 - x) dollars.
Now, we can calculate the interest earned from each investment:
Interest earned from the amount invested at 6% = x * 6% = 0.06x dollars.
Interest earned from the amount invested at 8% = (4000 - x) * 8% = 0.08(4000 - x) dollars.
According to the given information, the total yearly interest amount is $260. So we can write the following equation:
0.06x + 0.08(4000 - x) = 260
Now, we can solve this equation to find the value of x:
0.06x + 0.08 * 4000 - 0.08x = 260
0.06x + 320 - 0.08x = 260
-0.02x + 320 = 260
-0.02x = 260 - 320
-0.02x = -60
x = (-60) / (-0.02)
x = 3000
Therefore, $3000 was invested at 6%.