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Let x be the amount invested at 6%, in dollars.
Then the amount invested at 10%, is 2x dollars.
The 6% investment produces the interest of 0.06x dollars.
The 10% investment produces the interest of 0.1*(2x) dollars.
The total interest is
0.06x + 0.1*(2x) = 780 dollars.
Simplify and solve for x
0.06x + 0.2x = 780
0.26x = 780
x = = 3000.
Answer. $3000 invested at 6%; 2*3000 = 6000 dollars invested at 10%.
CHECK. 0.06*3000 + 0.1*6000 = 780 dollars. ! Correct !.
Solved.
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It is a standard and typical problem on investments.
If you need more details, or if you want to see other similar problems solved by different methods, 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.