Two investments totaling $50,000 produce an annual income of $3745. One investment yields 8% per year, while the other yields 7% per year. How much is invested at each rate?

Answer 1

we need a system of equations.

x + y = 50000

.08x + .07y = 3745

(It doesn't matter which percent goes with x or y- we'd just get the answers reversed).

I'm also going to multiply the 2nd equation by 100 to get rid of the pesky decimals.

8x + 7y = 374500

Now, let's solve the first equation for x.

x = 50000 - y

Next, we substitute the right side for x in the 2nd equation

8(50000 - y) + 7y = 374500

400000 - 8y + 7y = 374500

-y = -25500

{y = 25500}

x = 50000 - 25500 = 24500

{x=24500}

so $24500 is invested at rate of 8%

and $25500 is invested at the rate of 7%