Joan Arlington has twice as much money invested at 5% simple annual interest as she does at 4%. If her yearly income from the two investments is $378, how much does she have at each rate?
.05(2x) + .04(x) = 378
solve for x and that is the amount at 4% and double x to find the amount at 5%
To solve this problem, let's create an equation based on the given information.
Let's assume Joan Arlington has x dollars invested at 4% interest rate. According to the problem, she has "twice as much money invested at 5%." Therefore, she has 2x dollars invested at 5% interest rate.
The yearly income from the two investments can be calculated by multiplying the amount invested by the interest rate and adding them together.
For the investment at 4%, the income would be:
Income from 4% investment = (x) * (4/100) = 0.04x
For the investment at 5%, the income would be:
Income from 5% investment = (2x) * (5/100) = 0.10x
According to the problem, the total yearly income from both investments is $378. We can use this information to create an equation:
0.04x + 0.10x = 378
Now, we can solve this equation to find the value of x, which represents the amount invested at 4% interest rate.
0.04x + 0.10x = 378
0.14x = 378
x = 378 / 0.14
x = 2700
So Joan Arlington has $2700 invested at 4% interest rate.
Now, we can find the amount invested at 5% interest rate:
2x = 2 * 2700
2x = 5400
Therefore, Joan Arlington has $5400 invested at 5% interest rate.
To summarize:
- Joan Arlington has $2700 invested at 4% interest rate.
- Joan Arlington has $5400 invested at 5% interest rate.