SOLUTION: Last year, Lucy had $10,000 to invest. He invested some of it in an account that paid 9% simple interest per year, and he invested the rest in an account that paid 8% simple intere

Algebra ->  Finance -> SOLUTION: Last year, Lucy had $10,000 to invest. He invested some of it in an account that paid 9% simple interest per year, and he invested the rest in an account that paid 8% simple intere      Log On


   

Question 1189733: Last year, Lucy had $10,000 to invest. He invested some of it in an account that paid 9% simple interest per year, and he invested the rest in an account that paid 8% simple interest per year. After one year, he received a total of $820 in interest. How much did he invest in each account?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

        Instead of doing your homework for you, I'll do another one
                  exactly like it with different numbers.



Robert invested $10000 in two different accounts, one at 6% annual interest and the other at 9%.
How much did he invest in each account to get a yearly interest of $810?
~~~~~~~~~~~~~~ 

Let x = amount at 9%, in dollars.

Then the amount at 6% is the rest (10000-x) dollars.



The interest from the 9% amount is 0.09*x  dollars.

The interest from the 6%   amount is 0.06*(10000-x)   dollars.



Your equation is

    interest + interest      = total interest,   or


    0.09*x  + 0.06*(10000-x) = 810   dollars.


From the equation, express x and calculate the answer


    x = %28810+-+0.06%2A10000%29%2F%280.09-0.06%29 = 7000.


Answer.  The amount at 9% is $7000;  the rest  $10000-$7000 = $3000 is the amount at 6%.


Check.   0.06*3000 + 0.09*7000 = 810 dollars.   ! Correct !

Solved.

                Now do yours the same way.


-----------------

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.