Splitting investments. Joan had $3,000 to invest. She invested part of it in an investment paying 8% and the remainder in an investment paying 10%. If the total income on three investments was $290, than how much did she invest at each rate?
amount invested at 8% --- x
amount invested at 10% -- 3000-x
.08x + .10(3000-x) = 290
.08x + 300 - .1x = 290
-.02x = -10
x = -10/-.02 = 500
so $500 invested at 8% and 2500 invested at 10%
Investment. Part of $25,000
Well, let's figure this out, and hopefully, my answer will not be a joke!
Let's say Joan invested x dollars at 8%. So, the amount invested at 10% would be $3000 - x (since she invested the remainder).
Now, we can calculate the income from each investment. The income from the investment at 8% would be 8% of x, which is 0.08x. The income from the investment at 10% would be 10% of ($3000 - x), which is 0.1(3000 - x).
According to the problem, the total income from the investments is $290. Therefore, we can set up the following equation:
0.08x + 0.1(3000 - x) = 290.
Now, let's solve for x:
0.08x + 0.1(3000 - x) = 290
0.08x + 300 - 0.1x = 290
-0.02x = -10
x = -10 / (-0.02)
x = 500.
Hey, there we have it! Joan invested $500 at 8% and $2500 at 10%.
Now, that's no joke!
Let's assume Joan invested x dollars at 8% and (3000 - x) dollars at 10%.
The income from the investment at 8% is given by (x * 8%) = 0.08x dollars.
The income from the investment at 10% is given by ((3000 - x) * 10%) = 0.1(3000 - x) dollars.
According to the problem, the total income from the investments is $290, so:
0.08x + 0.1(3000 - x) = 290
Now we can solve for x.
0.08x + 0.1(3000 - x) = 290
0.08x + 300 - 0.1x = 290
-0.02x + 300 = 290
-0.02x = -10
x = -10 / -0.02
x = 500
Therefore, Joan invested $500 at 8% and ($3000 - $500) = $2500 at 10%.
To solve this problem, we need to set up a system of equations based on the given information.
Let's assume that Joan invested $x in the investment paying 8% and $(3000 - x) in the investment paying 10%.
According to the problem, the interest earned from the 8% investment can be calculated as 0.08x, and the interest earned from the 10% investment can be calculated as 0.1(3000 - x).
The total income from both investments is given as $290. So, we can write the equation:
0.08x + 0.1(3000 - x) = 290
Now, let's solve this equation step by step.
Distribute 0.1 to (3000 - x):
0.08x + 0.1(3000) - 0.1(x) = 290
Multiply 0.1 by 3000:
0.08x + 300 - 0.1x = 290
Combine like terms:
0.08x - 0.1x + 300 = 290
Combine the x terms:
-0.02x + 300 = 290
Subtract 300 from both sides:
-0.02x = -10
Divide by -0.02 to solve for x:
x = (-10) / (-0.02)
x = 500
Therefore, Joan invested $500 at a rate of 8% (0.08) and $(3000 - 500) = $2500 at a rate of 10% (0.1).