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%.
Algebra ->
Customizable Word Problem Solvers
-> Finance
-> 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%.
Log On
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):
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.
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).
