Mrs. Brighton invested $30,000 and received a total of $2,300 in interest. If she invested part of the money at 10% and the remainder at 5%, then how much did she invest at each rate?
.10 x + .05 (30,000-x) = 2,300
10 x + 5 (30,000-x)= 230,000
2 x + (30,000 - x ) = 46,000
x + 30,000 = 46,000
you take it from there
Assume that the money was left on deposit for one year. They should have told you that.
If x was invested at 10%, 30,000- x was invested at 5%
x * 0.10 + (30,000 -x) * 0.05 = 2300
0.1 x + 1500 - .05x = 2300
0.05 x = 800
x = 16,000 (invested at 10%)
(30,000 - x) = 14,000 invested at 5%
To find out how much Mrs. Brighton invested at each rate, we need to set up a system of equations.
Let's assume Mrs. Brighton invested x amount of money at 10% interest rate and the remaining amount, which is $30,000 - x, at 5% interest rate.
Now, we can calculate the interest earned from each investment:
Interest earned from the amount invested at 10% = x * 0.10 = 0.1x
Interest earned from the amount invested at 5% = (30,000 - x) * 0.05 = 1500 - 0.05x
According to the given information, the total interest earned is $2,300. Therefore, we can write the equation:
0.1x + (1500 - 0.05x) = 2300
Now, let's solve this equation to find the value of x:
0.1x + 1500 - 0.05x = 2300
0.05x = 2300 - 1500
0.05x = 800
x = 800 / 0.05
x = 16,000
So, Mrs. Brighton invested $16,000 at a 10% interest rate. Now, to find out how much she invested at 5%, we can subtract this amount from the total investment:
30,000 - 16,000 = $14,000
Therefore, Mrs. Brighton invested $16,000 at 10% and $14,000 at 5%.