SOLUTION: You invest some money at 8% and half as much at 5%, you earn $3150 in annual interest, how much did you invest at each rate?

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Interest(I) equals Principal(P) times Rate(R) times Time(T) (Note: In this problem T=1 year)
Let P=amount invested at 8%
Interest at 8%=(P)(0.08)(1)=0.08P
Then P/2=amount invested at 5%
Interest at 5%=(P/2)(0.05)(1)=0.025P
Now we are told that the interest accrued at 8% plus the interest accrued at 5% equals $3150. So, our equation to solve is:
0.08P+0.025P=3150 collect like terms
0.105P=3150 divide both sides by 0.105
P=$30,000------------------------------amount invested at 8%
P/2=(30,000/2)=$15,000---------------------amount invested at 5%
CK
0.08*30,000+0.05*15,000=3150
2400+750=3150
3150=3150

Hope this helps----ptaylor