Question

Emma has half of her investments in stock paying an 11% dividend and the other half in stock paying 14% interest if her total annual is 460 how much does she have invested?

Answer 1

Emma has $3680 invested.

Step-by-step explanation:

To find out how much Emma has invested, we can set up an equation and solve for the unknown. Let's say Emma has x dollars invested, which means she has half of that amount in stock paying an 11% dividend, and the other half in stock paying a 14% interest.

The amount of money invested in the first stock is 0.5x, and the amount invested in the second stock is also 0.5x. We can then calculate the annual income from each stock by multiplying the amount invested by the respective percentages:

Annual income from first stock = 0.11 * 0.5x = 0.055x

Annual income from second stock = 0.14 * 0.5x = 0.07x

The total annual income from both stocks is $460, so we can set up the equation:

0.055x + 0.07x = $460

Combining like terms, we get: 0.125x = $460

Dividing both sides by 0.125, we find that x = $3680.

Therefore, Emma has $3680 invested.

Answer 2

Given that half of her investments in a 11% dividend and the other half in a stock paying 14% interest.

Let the total investment be 2x dollars. So, x is invested in 11% dividend and x in a stock paying 14% interest.

Interest on both the investment is given below:

`\begin{gathered} 0.11x+0.14x=460 \\ 0.25x=460 \\ (0.25x)/(0.25)=(460)/(0.25) \\ x=1840 \end{gathered}`

So, the total investment is 2x = 2(1840) = $3680.