Question 1125428: You wish to invest $1600 over one year in two accounts paying 5% and 6% annually. How much should you invest in each to earn $89?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39617)   (Show Source):
Answer by ikleyn(52786)  (Show Source):
You can put this solution on YOUR website! .
Let x be the amount invested at 6%, in dollars.
Then the amount invested at 5% is the rest (1600-x) dollars.
Your basic equation is THIS:
interest + interest = total interest, or
0.06*x + 0.05*(1600-x) = 89.
0.06x + 0.05*1600 - 0.05x = 89
0.01x = 89 - 0.05*1600 ====> x =  = 900.
Answer. $900 should be invested at 6% and the rest 1600 - 900 = 700 dollars should be invested at 5%.
Check. 0.05*700 + 0.06*900 = 89 dollars. ! Correct !
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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!
The algebraic solution method for this kind of problem is fine.
But if you are working a lot of these problems, here is a method that will get you to the answer faster and with much less work. (I am good at mental arithmetic; solving this problem takes me about 5 seconds by this method.)
(1) The interest at 5% would be $80; the interest at 6% would be $96.
(2) Since $89 is 9/16 of the way from $80 to $96, 9/16 of the money should be invested at the higher rate.
(3) 9/16 of $1600 is $900.
ANSWER: $900 at 6%; $700 at 5%.
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