# Word problem find equations then solve

1. Mar 26, 2009

### synergix

1. The problem statement, all variables and given/known data

A certain amount of money saved for 1 year at a certain annual interest rate(simple interest) yielded 19.36$in interest. if we had added$66 to the principal and reduced the interest rate by 3 percentage point(s), the interest would have been the same, Find the principal and the rate.

2. Relevant equations

(1)$19.36= PR (2)$19.36=(P+\$66)(R-0.03)

3. The attempt at a solution

I solved (1) for P then substituted that into equation (2)and I got a complex answer so I must have incorrectly formed the equations any help?

2. Mar 26, 2009

### CompuChip

If I solve those equations I get a real answer which seems reasonable too. You must have incorrectly manipulated them.
Can you try typing out your calculation? If you don't spot the error while typing it, we might be able to help you find it.

3. Mar 26, 2009

### synergix

Ok here ya go.

first I solved (1) for R
R=19.36/P
Then I put that into (2)
19.36=(P+66)((19.36/P)-0.03)
(19.36=19.36-0.03P+1277.76/P-1.98)P
19.36P-19.36P=-0.03P-1.98P+1277.76
Then I divided by -0.03

0=P^2+66P-42529

and I found my mistake.... when I used the quadratic formula and multiplied -4ac I kept it negative and therefore ended up with a large negative square root and an imaginary answer D'oh
THX!

4. Mar 26, 2009

P=176 r=0.11