Question 1101355
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$15,074 is invested part at 14% and the rest at 5%. If the interest earned from the amount invested at 14% exceeds the interest 
earned from the amount invested at 5% by $1694.07 how much is invested at each rate? Round to two decimal places if necessary
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<pre>
From the condition, you have THIS system of 2 equations in 2 unknowns

    x +     y = 15074            (1)    (counting investments)
0.14x - 0.05y =  1694.07         (2)    (the difference between earnings)


To make your calculations easier, multiply eq(2) by 100 (both sides). The modified system is

    x +     y = 15074            (3)   
  14x -    5y = 169407           (4)  


Now multiply eq(3) by 5. The modified system takes the form

   5x +    5y = 5*15074          (5)
  14x -    5y = 169407           (4)  


Next add the equations (5) and (6) (both sides).  The terms with 5y will cancel each other, and you will get a single equation for x:


  19x = 5*15074 + 169407 = 244777.

    x = {{{244777/19}}} = 12883.


<U>Answer</U>.  It was invested $12883 at %14.  The rest 15074 - 12883 = 2191 was invested at  5%.


<U>Check</U>.  0.14*12883 - 0.05*2191 = 1694.07.   ! Correct !
</pre>

Solved.


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On investment problems, see 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.


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 "<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.



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Be aware !  Writing by @richwmiller was heavily incorrect.