Math Problem Statement

Indigo makes two separate investments, one paying
6 percent and the other paying
8 percent simple interest per year. She invests a total of
$ 7100 , and her annual interest earnings are
$ 508 . How much did she invest at each rate?

Solution

Let the amount Indigo invested at 6% be denoted as xx, and the amount invested at 8% be denoted as 7100x7100 - x (since her total investment is $7100).

The total interest earned in one year is $508, and we know the formula for simple interest is:

Interest=Principal×Rate×Time\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}

Since the time is 1 year, we can simplify the formula to:

Interest=Principal×Rate\text{Interest} = \text{Principal} \times \text{Rate}

Now, set up two equations based on the two investments:

\text{Interest from the 6% investment} = x \times 0.06 \text{Interest from the 8% investment} = (7100 - x) \times 0.08

The total interest from both investments is $508, so:

x×0.06+(7100x)×0.08=508x \times 0.06 + (7100 - x) \times 0.08 = 508

Now, solve this equation:

0.06x+0.08(7100x)=5080.06x + 0.08(7100 - x) = 508 0.06x+5680.08x=5080.06x + 568 - 0.08x = 508 0.02x+568=508-0.02x + 568 = 508 0.02x=508568-0.02x = 508 - 568 0.02x=60-0.02x = -60 x=600.02x = \frac{-60}{-0.02} x=3000x = 3000

So, Indigo invested $3000 at 6%. The remaining amount is:

71003000=41007100 - 3000 = 4100

Thus, she invested $4100 at 8%.

Summary:

  • Indigo invested $3000 at 6%.
  • She invested $4100 at 8%.

Would you like more details, or have any questions?

Here are 5 related questions:

  1. What is the formula for simple interest?
  2. How does compound interest differ from simple interest?
  3. If Indigo had invested at 7% instead of 6%, how would her total earnings change?
  4. What happens if she invests for multiple years under simple interest?
  5. How would the solution change if the interest rates were swapped?

Tip: When solving for unknowns, organizing your equations clearly can help avoid errors and speed up the process.

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Math Problem Analysis

Mathematical Concepts

Algebra
Simple Interest

Formulas

Simple Interest: Interest = Principal × Rate × Time
Total Interest Equation: 0.06x + 0.08(7100 - x) = 508

Theorems

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Suitable Grade Level

Grades 9-12