Question 1119323: a women has a total of $12,00 to invest. she invested part of the money in an account that pays 9% per year and the rest in an account that pays 10% per year. if the interest earned in the first year is $1160, how much did she invest in each account ? she invested $? at 9% and $? at 10%
Answer by ikleyn(52772)   (Show Source):
You can put this solution on YOUR website! .
Let me start from editing your post, replacing $12,00 by $12,000, since it is obvious typo.
Now the corrected formulation is THIS:
a women has a total of $12,000 to invest. she invested part of the money in an account that pays 9% per year
and the rest in an account that pays 10% per year. if the interest earned in the first year is $1160,
how much did she invest in each account ? she invested $? at 9% and $? at 10%
Solution
Let x = the amount invested at 10%.
Then the amount invested at 9% is (12000-x) dollars.
The total interest is the sum of partial interests, i.e.
0.1x + 0.09*(12000-x) = 1160.
Simplify and solve for x:
0.1x + 0.09*12000 - 0.09x = 1160,
0.01x = 1160 - 0.09*12000 = 80
x =  = 8000.
Answer. $8000 was invested at 10 and the rest (12000-$8000) = $4000 was invested at 9%.
Check. 0.1*8000 + 0.09*4000 = 1160 dollars. ! Correct !
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It is a typical and standard problem on investment.
To see many other similar solved problems on investment, look into the lesson
- Using systems of equations to solve problems on investment
in this site.
You will find there different approaches (using one equation or a system of two equations in two unknowns), as well as
different methods of solution to the equations (Substitution, Elimination).
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic "Systems of two linear equations in two unknowns".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
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