Question 72419
Let x be the portion invested into the CD account (certificate of deposit)
Let y be the portion invested into the savings account.
Now we already know that x + y = 8000, so let's solve this equation for y.

x + y = 8000 => y = 8000 - x.

Now we know x is invested at 8% and y is invested at 6%.  To find the amount each makes at the end of the year we take x(.08) + x.  Note x(.08) is the amount of interest that is made on that amount at the end of the year.  So we add x to this amount to get the total of x at the end of the year.  Similarly for y, we have y(.06) + y.

Now let's re-write these equations.

x(.08) + x = x(1.08), and
y(.06) + y = y(1.06).

Now, since we know that 580 dollars was made on the TOTAL amount at the end of the year we know we end up with 8580.

Now we can write this:

x(1.08) + y(1.06) = 8580

Now, since we solved for y at the beginning, we can plug this value into this equation and solve for x.

x(1.08) + y(1.06) = 8580
x(1.08) + (8000-x)(1.06) = 8580 (multiply 8000-x by 1.06)
x(1.08) + 8480 - x(1.06) = 8580 (subtract 8480 from both sides)
x(1.08) - x(1.06) = 100 (subtract x terms on the left hand side)
x(.02) = 100 (divide both sides by .02)
x = 5000.  

Now we can plug this value into the original equation to solve for y.

5000 + y = 8000
y = 3000.

So, 5000 was invested into the CD and 3000 was invested into the savings account.

I hope this helps!!