Question 1188524
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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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<pre>
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     <=      {{{350/0.01}}} = 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.
</pre>

Solved.


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