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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?
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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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