Larry Mitchell invested part of his $ 30 comma 000 advance at 2 % annual simple interest and the rest at 5 % annual simple interest.  If his total yearly interest from both accounts was $ 1 comma 170​, find the amount invested at each rate.

Let the amount Larry invested at 2% interest be $ x $, and the amount invested at 5% interest be $ 30,000 - x $ since the total amount he invested is $30,000.

The simple interest formula is given by:

\[
\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}
\]

Since the time is 1 year, the yearly interest from the two accounts can be written as:

\[
\text{Interest from 2% account} = x \times 0.02
\]
\[
\text{Interest from 5% account} = (30,000 - x) \times 0.05
\]

The total interest from both accounts is $1,170, so we can set up the equation:

\[
x \times 0.02 + (30,000 - x) \times 0.05 = 1,170
\]

Now, let's solve this equation:

\[
0.02x + 0.05(30,000 - x) = 1,170
\]

Expanding the equation:

\[
0.02x + 0.05 \times 30,000 - 0.05x = 1,170
\]
\[
0.02x + 1,500 - 0.05x = 1,170
\]

Combining like terms:

\[
-0.03x + 1,500 = 1,170
\]

Subtracting 1,500 from both sides:

\[
-0.03x = -330
\]

Dividing both sides by -0.03:

\[
x = \frac{-330}{-0.03} = 11,000
\]

So, Larry invested $11,000 at 2%. The rest of the investment is:

\[
30,000 - 11,000 = 19,000
\]

Thus, Larry invested $11,000 at 2% interest and $19,000 at 5% interest.

---

Would you like more details on this solution or have any questions?

Here are 5 related questions to think about:
1. What if Larry invested the entire $30,000 at 5%? How much interest would he earn?
2. What would happen to the total interest if the rates were reversed (2% for $19,000 and 5% for $11,000)?
3. How would the result change if the total investment was $40,000 instead of $30,000?
4. What is the formula for compound interest, and how does it differ from simple interest?
5. How much interest would Larry earn in 2 years with the same investments?

**Tip**: Always remember that with simple interest, interest is calculated only on the original principal, not on accumulated interest!

Larry Mitchell invested part of his $30,000 advance at 2% annual simple interest and the rest at 5% annual simple interest. If his total yearly interest from both accounts was $1,170, find the amount invested at each rate.

Larry invested $30,000, with part at 2% and the rest at 5% annual simple interest. The total yearly interest was $1,170. Learn how to calculate the amounts invested at each rate using algebraic methods, simple interest formulas, and solving linear equations. Suitable for Grades 9-10 students.

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