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Question 1114410: mr. smith invests part of $8000 at 4% and the remainder at 6%. the annual effective rate on his total investment is 4.4%. find the amount invested at each rate.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
0.04*x + 0.06*(8000-x) = 0.044*8000
0.04x + 480 - 0.06x = 0.044*8000
-0.02x = 0.044*8000 - 480 = -128 ====> x =  = 6400.
Answer. $6400 was invested at 4% and the rest (8000-6400) = 1600 was invested at 6%.
Check. 0.04*6400 + 0.06*1600 = 352 dollars.
8000*0.044 = 352 dollars, the same value. ! Correct !
Solved.
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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.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Obviously, if all the money were invested at 4%, the effective overall rate would be 4%; if it were all invested at 6%, the effective rate would be 6%.
It should also be intuitive that if the money were split evenly between 4% and 6%, the effective rate would be 5%.
In general, where the effective rate lies between 4% and 6% exactly determines the ratio in which the money must be split between the two investments.
The effective rate, 4.4%, is 1/5 of the way from 4% to 6%. (4.4-4 = 0.4; 6-4 = 2; 0.4/2 = 0.2 = 1/5). That means exactly 1/5 of the money was invested at the higher rate.
Answer: 1/5 of the $8000 = $1600 at 6%; the rest ($6400) at 4%.
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