Question 55083
Big picture...why didn't Stan invest all his money at 17%? Don't take investment advice from Stan. 


Ok..let's make up some variables to start:

We'll call x the amount that Stan invested at 8% and y the amount that he invested at 17%. 

We know he invested 5 bills, so we get the following equation:

{{{x + y = 5000}}}

Also, his combined interest income was $490. So 8% of x plus 17% of y must be $490. In math-speak:

{{{.08x+.17y = 490.}}}

Here, we've got the following system of equations:
{{{x + y = 5000}}}
 
{{{.08x+.17y = 490.}}}

I'll use the substitution method and solve for x in the first equation
{{{x + y = 5000}}}
{{{x = 5000-y}}}

Now, I'll plug that into the second equation
{{{.08(5000-y)+.17y = 490}}}
{{{400-.08y+.17y = 490}}}
{{{400+.09y = 490}}}
{{{.09y = 90}}}
{{{y = 1000}}}

Alright! y = 1000! 
if we plug that into {{{x = 5000-y}}}, we get
{{{x = 5000-1000}}}
{{{x = 4000}}}

Ok. My answers are different than yours. I'll check my work. 

CHECK:
Using the second original equation:
{{{.08x+.17y = 490}}}
{{{.08(4000) +.17(1000) = 490}}}
{{{320 + 170 = 490}}}
{{{490 = 490}}} Check!

Stan invested $4000 at 8%. Dumbass. Don't let Stan run your investments.