SOLUTION: Stan invested $17,000, part at 18% and part at 4%. If the total interest at the end of the year is $1,380, how much did he invest at each rate?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Stan invested $17,000, part at 18% and part at 4%. If the total interest at the end of the year is $1,380, how much did he invest at each rate?       Log On


   

Question 108124: Stan invested $17,000, part at 18% and part at 4%.
If the total interest at the end of the year is $1,380, how much did he invest at each
rate?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let's call the part he invested at 18%, E, and the part he invested at 4%, F.
Then you know that,
1.E%2BF=17000
2.0.18E%2B0.04F=1320
Use 1. to solve for E in terms of F.
1.E%2BF=17000
E=17000-F
Now substitute that into equation 2 and solve for F.
2.0.18E%2B0.04F=1320
0.18%2817000-F%29%2B0.04F=1320
0.18%2817000%29-0.18F%2B0.04F=1320
3060-0.14F=1320
-0.14F=1320-3060
-0.14F=-1740
F=12428.57
From 1.
E=17000-F
E=17000-12428.57
E=4571.43
Verify your answer using equation 2.
0.18E%2B0.04F=1320
0.18%284571.43%29%2B0.04%2812427.57%29=1320
822.86%2B497.10=1320
1319.96=1320 Close enough, round off error.
Good answer.
$4571.43 at 18%, $12428.57 at 4%.