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 , and the amount invested at 8% be denoted as (since her total investment is $7100).
The total interest earned in one year is $508, and we know the formula for simple interest is:
Since the time is 1 year, we can simplify the formula to:
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:
Now, solve this equation:
So, Indigo invested $3000 at 6%. The remaining amount is:
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:
- What is the formula for simple interest?
- How does compound interest differ from simple interest?
- If Indigo had invested at 7% instead of 6%, how would her total earnings change?
- What happens if she invests for multiple years under simple interest?
- 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
-
Suitable Grade Level
Grades 9-12
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