SOLUTION: Jun invests thirty five thousand , part at 8% and part at 9%. What is the most that can be invested at 8% to make at least two thousand eight hundred interest per year?

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Question 1188524: Jun invests thirty five thousand , part at 8% and part at 9%. What is the most that can be invested at 8% to make at least two thousand eight hundred interest per year?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Jun invests thirty five thousand , part at 8% and part at 9%.
What is the most that can be invested at 8% to make at least
two thousand eight hundred interest per year?
~~~~~~~~~~~~~~ 

x invested at 8%;  (35000-x) invested at 9%.


Write the inequality

    0.08*x + 0.09*(35000-x) >= 2800


Simplify and find x

    (0.08 - 0.09)x >= 2800 - 0.09*35000

        -0.01x     >=     -350


Change the sign in both sides; replace the inequality sign by the opposite

         0.01x     <=      350

             x     <=       = 35000.


The maximum value of x, satisfying this inequality is x = 35000.


Notice that 0.08*35000 = 2800 exactly and precisely,

so, Jun must invest the total amount of $35000 at 8% to satisfy the condition.

Solved.

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This problem is intended to teach a student playing with the notions  " at least "  and  " at most "  in one package . . .



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


The problem doesn't really make sense....

All $35,000 invested at 8% will yield $2800 interest.

The question asks for the MAXIMUM AMOUNT he can invest at 8% and make AT LEAST $2800 interest is $35,000. So....

ANSWER: $35,000

Of course, the total interest will be more than $2800 if some of the money is invested at 9%.
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