Question 1119323
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Let me start from editing your post, replacing $12,00 by $12,000,  since it is obvious typo.


Now the corrected formulation is THIS:


<pre>
    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%
</pre>


<U>Solution</U>


<pre>
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 = {{{80/0.01}}} = 8000.


<U>Answer</U>.  $8000 was invested at 10 and the rest (12000-$8000) = $4000 was invested at 9%.


<U>Check</U>.  0.1*8000 + 0.09*4000 = 1160 dollars.   ! Correct !
</pre>

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It is a typical and standard problem on investment.


To see many other similar solved problems on investment, &nbsp;look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Using-systems-of-equations-to-solve-problems-on-investment.lesson>Using systems of equations to solve problems on investment</A>

in this site.


You will find there different approaches &nbsp;(using one equation or a system of two equations in two unknowns), &nbsp;as well as 
different methods of solution to the equations &nbsp;(Substitution, &nbsp;Elimination).


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this online textbook under the topic &nbsp;"<U>Systems of two linear equations in two unknowns</U>".



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.