Two investments totaling $36,000$36,000 produce an annual income of $2715$2715. One investment yields 6%6% per year, while the other yields 9%9% per year. How much is invested at each rate?
Question
Two investments totaling 36,000 produce an annual income of 2715. One investment yields 6%6% per year, while the other yields 9%9% per year. How much is invested at each rate?
Solution
Let's denote the amount invested at 6% as x and the amount invested at 9% as y.
From the problem, we know two things:
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The total amount invested is $36,000. So, we can write this as an equation: x + y = 36,000.
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The total annual income from both investments is $2715. The income from the first investment is 6% of x and the income from the second investment is 9% of y. We can write this as another equation: 0.06x + 0.09y = 2715.
Now we have a system of two equations, and we can solve it step by step:
Step 1: Multiply the first equation by 0.06 to make the coefficients of x in both equations the same:
0.06x + 0.06y = 2160.
Step 2: Subtract the new equation from the second equation:
0.03y = 555.
Step 3: Solve for y by dividing both sides by 0.03:
y = 18500.
Step 4: Substitute y = 18500 into the first equation:
x + 18500 = 36000,
x = 17500.
So, 18,500 is invested at 9%.
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