SOLUTION: A total of $2200 is invested, part at 5% and the rest at 3%. The annual income from the 3% account is $46 less than the income from the 5% account. Find the amount invested at 3%.

Question 1114760: A total of $2200 is invested, part at 5% and the rest at 3%. The annual income from the 3% account is $46 less than the income from the 5% account. Find the amount invested at 3%.
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.

Let x be the amount invested at 3%, in dollars.

Then the rest, (2200-x) was invested at 5%.


The annual interest from the 3% account is  0.03*x 

The annual interest from the 5% account is 0.05*(2200-x).


The condition says

0.03*x = 0.05*(2200-x) - 46  dollars.


Simplify and solve for x:

0.03x = 110 - 0.05x - 46

0.03x + 0.05x = 110 - 46

0.08x = 64  ====>  x =  =  = 800 dollars.


Answer.  $800 was invested at 3%.  The rest,  2200-800 = 1400 dollars was invested at 5%.


Check.   0.03*800 - 0.05*1400 = -46.    ! Correct !

Solved.

-----------------
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.

RELATED QUESTIONS
a man invested $25,000, part of it was invested at 3% and the rest at 4%. the total... (answered by checkley77)

a man invested $25,000, part of it was invested at 3% and the rest at 4%. the total... (answered by checkley77)

Investment Problem A man invested Php 6,000, part of it at 3% and the rest at 4%. The... (answered by Boreal,greenestamps)

A man invested Php 6,000, part of it at 3% and the rest at 4%. The total annual income... (answered by ikleyn)

A man invested part of $10,000 at 6% and rest at 7%. The annual income from 7% invested... (answered by stanbon)

Larry Mitchell invested part of his $30000 advance at 3% annual interest and the rest at... (answered by ewatrrr)

Larry Mitchell invested part of his $30000 advance at 3% annual interest and the rest at... (answered by addingup)

A man invested part of P20,000 at 18% and the rest at 16%. The annual income from 16%... (answered by Theo,MathTherapy)

a small company invested $20,500 such that a part of the money is in an account with a 4% (answered by lwsshak3)