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Let x be an amount invested at 10.2%.
Then the amount invested at 12% is (3x) dollars, according to the condition.
The interest from the 10.2% account is 0.102*x dollars.
The interest from the 12% account is 0.12*(3x) dollars.
Your equation is
interest + interest = total interest, or
0.102*x + 0.12*(3x) = 462 dollars.
From the equation, express x and calculate the answer
x = = 1000 dollars.
Answer. The amount at 10.2% is $1000; the amount at 12% is 3 times it, i.e. = $3000.
Check. 0.102*1000 + 0.12*3000 = 462 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.