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Question 1180473: Joseph has $12500 to invest in two different accounts. Account 1 pays 9% interest and account 2 pays 12%. After a year, the interest paid by account 2 is twice the interest paid by account 1. How much money did Joseph invest in each account?
Found 2 solutions by ikleyn, mananth:
Answer by ikleyn(52777)   (Show Source):
You can put this solution on YOUR website! .
account 1 = x
account 2 = (12500-x)
Your equation is
2*(0.09x) = 0.12*(12500-x)
Simplify and solve
0.18x = 0.12*12500 - 0.12x
0.18x + 0.12x = 0.12*12500
x =  = 5000.
ANSWER. Account 1 is $5000; account 2 is the rest $7500.
CHECK. 0.09*5000 = 450 dollars, interest paid by account 1.
0.12*7500 = 900 dollars, interest paid by account 2.
The ratio of interest is 2, in the right order. ! Correct !
Solved, answered, checked and carefully explained.
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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.
Answer by mananth(16946)  (Show Source):
You can put this solution on YOUR website!
Joseph has $12500 to invest in two different accounts.
x in account 1
12500-x in account 2
Account 1 pays 9% interest and account 2 pays 12%.
9%x interest in account 1
12%(12500-x) in account 2
Account 1 pays 9% interest and account 2 pays 12%.
12%(12500-x) =2*9%x
multiply equation by 100
12(12500-x) =18x
150000 -12x =18x
30x = 150000
x=5000
$5000 at 9%
$7500 at 12%
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