Question
15. Marty Lister invested \( \$ 9000 \) in stocks and bonds. The stocks paid \( 5 \% \) and the bonds \( 8 \% \), giving an annual income of \( \$ 525 \). How much did he invest in bonds?
Ask by Henry Norris. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Marty invested $2500 in bonds.
Solution
Let the amount invested in bonds be B and the amount invested in stocks be 9000 - B. Since the bonds yield 8% and the stocks yield 5%, the total annual income from the investments is given by:
0.05(9000 - B) + 0.08B = 525
First, multiply out the first term:
450 - 0.05B + 0.08B = 525
Combine like terms:
450 + 0.03B = 525
Subtract 450 from both sides:
0.03B = 75
Divide both sides by 0.03:
B = 75 / 0.03 = 2500
Thus, Marty invested $2500 in bonds.
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Simplify this solution The Deep Dive
To find out how much Marty invested in bonds, let's use a bit of algebra! Let \( x \) be the amount invested in bonds. Thus, the amount invested in stocks would be \( 9000 - x \). The income from stocks would be \( 0.05(9000 - x) \) and from bonds \( 0.08x \). The total income equation can be set up as follows: \[ 0.05(9000 - x) + 0.08x = 525. \] Now, simplify and solve for \( x \): \[ 450 - 0.05x + 0.08x = 525, \] \[ 0.03x = 525 - 450, \] \[ 0.03x = 75, \] \[ x = \frac{75}{0.03} = 2500. \] So, Marty invested \( \$ 2500 \) in bonds. Now, to find out how much he invested in stocks: \[ 9000 - 2500 = 6500. \] Thus, he invested \( \$ 6500 \) in stocks.
