SOLUTION: Amy invests $1500 in one account and $1900 in an account paying 3 % higher interest. At the end of one year she had earned $261 in interest. At what rates did she invest? 1500 i

Question 1129650: Amy invests $1500 in one account and $1900 in an account paying 3 % higher interest. At the end of one year she had earned $261 in interest. At what rates did she invest?
1500 invested at -
1900 invested at-
Found 2 solutions by Boreal, greenestamps:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
interest for 1500 is x
interest for 1900 is x+3
1500*x/100=15x
1900*(x+3)/100=19x+57
that sum is 261
34x=204
x=6% for $1500=$90
X+3 is 9% for $1900=$171
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Here is a solution using some logical reasoning and some mental arithmetic, instead of formal algebra.

First consider the "extra" 3% that is earned on the $1900 investment. The amount of interest there is .03($1900) = $57.

The remaining amount of interest is $261-$57 = $204. That is the amount of interest on the whole investment of $3400. Since we have accounted for the interest from the extra 3% on the second investment, that $204 interest is now all at the lower rate.

= 6%

The $1500 was invested at 6%; the $1900 was invested at 6%+3% = 9%.
RELATED QUESTIONS
Tiana invests $1900 in one account and $1400 in an account paying 3 % higher interest. At (answered by MathLover1)
Brianna invests $2400 in one account and $1900 in an account paying 2 % higher interest.... (answered by macston)
Whintney invests $1900in one account and $1600 in an account paying 1% higher interest.... (answered by Fombitz)
Emma invests $900 in one account and $1800 in an account paying 3 % higher interest. At... (answered by stanbon)
Mackenzie invests $800 in one account and $2400 in an account paying 3 % higher interest. (answered by stanbon)
Naomi invests $1800 in one account and $800 in an account paying 1 % higher interest. At... (answered by ikleyn)
Natasha invests $2100 in one account and $1400 in an account paying 2 % higher interest.... (answered by Alan3354,ikleyn,greenestamps)
Taylor invests $800 in one account and $1600 in an account paying 4 % higher interest. At (answered by mananth)
Destiny invests $2500 in one account and $900 in an account paying 4 % higher interest.... (answered by jorel1380)