SOLUTION: A maninvested $1000, part at 5% ant the rest at 6%. His total annual income was $53. How much did he invest at each rate?

Question 137587: A maninvested $1000, part at 5% ant the rest at 6%. His total annual income was $53. How much did he invest at each rate?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Interest(I) equals Principal(P) times Rate(R) times Time(T) or I=PRT
($ understood)
Let x=amount invested at 6%
Then 1000-x=amount invested at 5%
Interest at 6% =x*0.06*1=0.06x
Interest at 5%=(1000-x)*0.05*1=0.05(1000-x)
Now we are told that the total interest was $53, so:
0.06x+0.05(1000-x)=53 get rid of parens
0.06x+50-0.05x=53 subtract 50 from each side
0.06x+50-50-0.05x=53-50 collect like terms
0.01x=3 divide both sides by 0.01
x=$300--------------------------------amount invested at 6%
1000-x=1000-300=$700------------------amount invested at 5%
CK
Interest at 6%=300*0.06*1=$18
Interest at 5%=700*0.05*1=$35
$35+$18=$53
$53=$53

Hope this helps---ptaylor
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