Question 102484
I need help setting up the following problem:
You invest $6000 in two accounts payinhg 6% and 9% annual interest, respectively. At the end of the year, the accounts earn the same interest. How much was invested at each rate?

Let's say you invest X at 6% and Y at 9%. 
You know that 
1.{{{X+Y=6000}}}
You also know that the interest for each is the same
{{{I[x]=X*6/100=INT}}}
{{{I[y]=Y*9/100=INT}}}
Set them equal to each other.
{{{X*6/100=Y*9/100}}}
2.{{{X*6=Y*9}}}
Now you have two equations with two unknowns (X and Y).
Use Equation (2) and solve for X.
{{{X=9*Y/6=3*Y/2}}}
Substitute into Equation (1)
1.{{{X+Y=6000}}}
{{{3*Y/2+Y=6000}}}Substitute
{{{3*Y+2*Y=12000}}}Multiply both sides by 2.
{{{5*Y=12000}}}Simplify.
{{{cross(5)*Y/cross(5)=12000/5}}}Multiplicative inverse of 5.
{{{Y=2400}}}
Use equation (1) 
{{{X+Y=6000}}}
{{{X=3600}}}
$3600 invested at 6%.
$2400 invested at 9%.
$216 made by each account.