Let's define two variables to represent the amounts Molly invested in stocks and bonds:
- Let \( x \) be the amount Molly invested in bonds.
- Let \( y \) be the amount Molly invested in stocks.
From the problem statement, we know two things:
1. The total amount invested in both stocks and bonds is $50,000.
2. The total profit from both investments is $8,700.
These can be represented by the following system of equations:
1. \( x + y = 50,000 \)
2. \( 0.15x + 0.18y = 8,700 \)
We need to solve this system to find the value of \( x \) (the amount invested in bonds).
We start by solving the first equation for \( y \):
\[ y = 50,000 - x \]
Next, let's substitute this expression for \( y \) in the second equation:
\[ 0.15x + 0.18(50,000 - x) = 8,700 \]
Distribute \( 0.18 \) in the equation:
\[ 0.15x + 9,000 - 0.18x = 8,700 \]
Combine like terms:
\[ -0.03x + 9,000 = 8,700 \]
Subtract \( 9,000 \) from both sides of the equation to isolate the term with \( x \):
\[ -0.03x = -300 \]
Divide both sides by \( -0.03 \):
\[ x = \frac{-300}{-0.03} \]
\[ x = 10,000 \]
So, Molly invested $10,000 in bonds.
To verify, let's calculate the amount she invested in stocks:
\[ y = 50,000 - x \]
\[ y = 50,000 - 10,000 \]
\[ y = 40,000 \]
Now let's check the total profit calculation:
\[ 0.15 \times 10,000 + 0.18 \times 40,000 \]
\[ 1,500 + 7,200 = 8,700 \]
The calculations are correct. Therefore, Molly invested $10,000 in bonds.
Molly invested $50,000 in various stocks and bonds. she earned 15% on the bonds and 18% on the stocks. If molly's total profit on both types of investment was $8,700, how much of the $50,000 did she invest in bonds?
1 answer
1 answer