SOLUTION: I am having trouble with word problems, Please help!! Nancy B. Kindy won $200,000 in a state lottery. She first paid income tax of 30% on the winnings. Of the rest, she invested

Question 125175This question is from textbook A Graphical Approach to College Algebra
: I am having trouble with word problems, Please help!!
Nancy B. Kindy won $200,000 in a state lottery. She first paid income tax of 30% on the winnings. Of the rest, she invested some at 1.5% and some at 4%, earning $4350 interest per year. How much did she invest at each rate.
THANK YOU! This question is from textbook A Graphical Approach to College Algebra

Found 2 solutions by stanbon, scott8148:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Nancy B. Kindy won $200,000 in a state lottery. She first paid income tax of 30% on the winnings. Of the rest, she invested some at 1.5% and some at 4%, earning $4350 interest per year. How much did she invest at each rate.
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Nancy had 0.70*200,000= $140,000 to invest.
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Let amt. invested at 1.5% be "x" ; interest on this is 0.015x dollars
Amt invested at 4% is "140000-x" ; interest is 0.04(140000-x)= 5600-0.04x
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EQUATION:
interest + interest = 4350
0.015x + 5600-0.04x = 4350
-0.025x = -1250
x = $50,000 (amt. invested at 1.5%)
140,000-x =$90,000 (amt invested at 4%)
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Cheers,
Stan H.
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
the amount remaining after 30% taxes is (100%-30%) of 200000, or .7*200000=140000

let x="amount @ 4%", so (140000-x)="amount @ 1.5%"

(.04)(x)+(.015)(140000-x)=4350 __ .04x+2100-.015x=4350 __ .025x=2250
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