Question 1178437
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part of $5,200 is invested at an annual rate of 7 1/2% and remainder is invested at an annual rate 5%. 
If the total number annual income from these two investments is $350, find the number of dollars 
invested at the 5% rate.
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<pre>

Let x be the amount (in dollars) invested at 5% rate.


Then the part invested at 7.5% is  (5200-x) follars.


Then you have this total interest equation


    0.05x + 0.075*(5200-x) = 350   dollars.


From the equation


    x = {{{(350-0.075*5200)/(0.05-0.075)}}} = 1600.


<U>ANSWER</U>.  The amount invested at 5% was 1600  dollars.


<U>CHECK</U>.  The total interest  0.005*1600 + 0.075*(5200-1600) = 3500  dollars.   ! Correct !
</pre>

Solved.


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It is a standard and typical problem on investments.


If you need more details,  &nbsp;or if you want to see other similar problems solved by different methods, &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.