SOLUTION: Sam’s annual interest from an investment is $225. If Sam had invested $600 more at an annual interest rate that was 1% less, the annual interest would have been $234. What are th

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Sam’s annual interest from an investment is $225. If Sam had invested $600 more at an annual interest rate that was 1% less, the annual interest would have been $234. What are th      Log On


   

Question 741167: Sam’s annual interest from an investment is $225. If Sam had invested $600 more at an annual interest rate that was 1% less, the annual interest would have been $234. What are the amount and the rate of his actual investment?
I have tried a few different things. I'm completely frustrated. This is my first time trying a tutor site, Thanks in advance for any help that you can give me! I know it involves a table, and I know the simple interest formula of I=Prt of course.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +r+ = the actual interest rate
+r+-+.01+ = the lower rate
+I+=+P%2Ar%2At+
+t+=+1+ year
--------------
given:
(1) +225+=+P%2Ar%2A1+
and
(2) +234+=+%28+P+%2B+600+%29%2A%28+r+-+.01+%29+
-------------------------------
(2) +234+=+P%2Ar+%2B+600r+-+.01P+-+6+
(2) +234+=+P%2A%28+r+-+.01+%29+%2B+600r+-+6+
(2) +P%2A%28+r+-+.01+%29+=+240+-+600r+
(2) +P+=+%28+40%2A%28+6+-+15r+%29+%29+%2F+%28+r+-+.01+%29+
----------------------------------
(1) +P+=+225%2Fr+
Substitute this back into (2)
(2) +225%2Fr+=+%28+40%2A%28+6+-+15r+%29+%29+%2F+%28+r+-+.01+%29+
(2) +225+=+40r%2A%28+6+-+15r+%29+%2F+%28+r+-+.01+%29+
(2) +225%2A%28+r+-+.01+%29+=+240r+-+600r%5E2+
(2) +225r+-+2.25+=+240r+-+600r%5E2+
(2) +-600r%5E2+%2B+15r+%2B+2.25+=+0+
(2) +-2400r%5E2+%2B+60r+%2B+9+=+0+
(2) +-800r%5E2+%2B+20r+%2B+3+=+0+
Use the quadratic formula
+r+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+-800+
+b+=+20+
+c+=+3+
+r+=+%28-20+%2B-+sqrt%28+20%5E2+-+4%2A%28-800%29%2A3+%29%29+%2F+%282%2A%28-800%29%29+
+r+=+%28-20+%2B-+sqrt%28+400+%2B+9600+%29%29+%2F+%28-1600%29+
+r+=+%28-20+%2B-+sqrt%28+10000+%29%29+%2F+%28-1600%29+
+r+=+%28+-20+-+100+%29+%2F+%28-1600%29+
+r+=+120+%2F+1600+
+t+=+.075+
The rate of the investment was 7.5%
and, since
(1) +225+=+P%2Ar%2A1+
(1) +P+=+225+%2F+.075+
(1) +P+=+3000+
The amount of the investment was $3,000
check:
(2) +234+=+%28+P+%2B+600+%29%2A%28+r+-+.01+%29+
(2) +234+=+%28+3000+%2B+600+%29%2A%28+.075+-+.01+%29+
(2) +234+=+3600%2A.065+
(2) +234+=+234+
OK