An executive invests $24,000, some at 6% and the rest 4% annual interest. If he receives an annual return of $1,260, how much is invested at each rate?

Answer 1

This is a problem with two variables and two equations:

Let x equal the amount of money invested at 6% annually and let y equal the amount of money invested at 4% annually.

(this is our first equation, we know that both amounts of money added together must total $24000)

x + y = 24000

(this is our second equation, we know that the money earned at 6% plus the money earned at 4% added together must equal $1260)

0.06x + 0.04y = 1260

Here is our set of equations:

0.06x + 0.04y = 1260

x + y = 24000

0.06x + 0.04y = 1260

x + y = 24000 (multiply the bottom equation by -0.06 so the x's will cancel)

0.06x + 0.04y = 1260

-0.06x -0.06 y = -1440 (now add the two equations and we get..)

-0.02y = -180 (divide both sides by -0.02)

y=9000 (since y is $9000, we can subtract that from the total amount of money invested to find x)

x = 24000-9000

x = 15000

Hope this helps!