A college student invested part of a $25,000 inheritance at 7% interest and the rest at 6%. If his annual interest is $1,671 how much did he invest at 6%? If I told you the answer is $8,000, in your own words, using complete sentences, explain how you would solve the problem.
Notice the key words here: in your own words.
A college student invested part of a $25,000 inheritance at 7% interest and the rest at 6%. If his annual interest is $1,670, how much did he invest at 6%?
Once you have answered the question above, answer the questions below. You must respond to both parts of this discussion question in order to receive full credit.
Explain how you approached this problem and the strategy/strategies you used to help guide your thinking.
To solve the problem, we need to use a system of equations. Let's assume the amount invested at 7% interest is x dollars, and the amount invested at 6% interest is y dollars. Given that the total inheritance the student invested is $25,000, we can write the first equation as x + y = 25,000.
Now, we know that the student earned $1,671 in interest annually. The interest earned on the investment at 7% is 0.07x, and the interest earned on the investment at 6% is 0.06y. Therefore, our second equation is 0.07x + 0.06y = 1,671.
To find how much the student invested at 6% interest, we're given that the answer is $8,000. Therefore, we can substitute y = $8,000 into the first equation: x + $8,000 = $25,000.
To solve for x, we subtract $8,000 from both sides: x = $25,000 - $8,000.
Simplifying, x = $17,000. Therefore, the college student invested $17,000 at 7% interest and $8,000 at 6% interest.