Question

rhianna invests $1200 in stock and bonds. the stock pays 9% interest and the bonds pay 6% interest. if the total annual interest is $96, how much is invested in the stock alone?
a $400
b $500
c $700
d $800

Explanation:

Step1: Define Variables

Let \( x \) be the amount invested in stocks (in dollars), then the amount invested in bonds is \( 1200 - x \) dollars.

Step2: Set Up Interest Equation

The interest from stocks is \( 0.09x \) (9% of \( x \)) and from bonds is \( 0.06(1200 - x) \) (6% of \( 1200 - x \)). The total annual interest is $96, so:

$$ 0.09x + 0.06(1200 - x) = 96 $$

Step3: Solve the Equation

First, expand the equation:

$$ 0.09x + 72 - 0.06x = 96 $$

Combine like terms:

$$ 0.03x + 72 = 96 $$

Subtract 72 from both sides:

$$ 0.03x = 24 $$

Divide both sides by 0.03:

$$ x = \frac{24}{0.03} = 800 $$

Answer:

$800 (Option D)