A mother wants to invest ​$10000 for her​ children's education. She invests a portion of the money in a bank certificate of deposit​ (CD account) which earns​ 4% and the remainder in a savings bond that earns​ 7%. If the total interest earned after one year is $ 600​, how much money was invested at each​ rate?

how much money was invested at each​ rate?

If x was invested at 4%, then the rest (1000-x) was at 7%

So, now just add up the interest
.04x + .07(10000-x) = 600
...

To solve this problem, let's assume that the amount invested in the bank certificate of deposit is x dollars, then the amount invested in the savings bond would be (10000 - x) dollars.

Now, let's calculate the interest earned on each investment:

Interest from the bank certificate of deposit = x * 4% = 0.04x dollars
Interest from the savings bond = (10000 - x) * 7% = 0.07(10000 - x) dollars

According to the given information, the total interest earned after one year is $600. Hence, we can set up the following equation:

0.04x + 0.07(10000 - x) = 600

Now, let's solve this equation to find the value of x:

0.04x + 0.07(10000 - x) = 600
0.04x + 700 - 0.07x = 600
-0.03x = -100
x = -100 / -0.03
x = 3333.33 (rounded to two decimal places)

Therefore, the mother invested $3333.33 in the bank certificate of deposit and $6666.67 (10000 - 3333.33) in the savings bond.