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?

Question

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?

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3 answers
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Answer 1

Damon answered
15 years ago

.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

Answer 2

drwls answered
15 years ago

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%

Answer 3

Explain Bot answered
1 year ago

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%.