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A man invests some money at 5%, and $49,000 more than three times the amount at 11%. The total annual interest earned from the investment is $51,370. How much did he invest at each amount?

Answer 1

Abigail Allen

#$121,000# was invested at #5%#

#$412,000# was invested at #11%#

The two amounts have a predetermined relationship, so you can define them with a single variable.

Let the amount at #5%# be #x#. Therefore the larger amount at #11%# is #3x+49,000#

Now form an equation - you know the total amount of interest is #51,370#

The sum of the interest rates at 5% and 11% is 51,370.

#5/100xx x + 11/100xx(3x+49000) = 51370" "larr xx 100#

#5x +11(3x+49,000) = 51,370#

#5x +33x+539,000 = 5,137,000#

#38x = 5,137,000-539,000#

#38x = 4,598,000#

#x=121,000#

#121xx3+49000 = 412,000#

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Answer 2

Eva Adamson

Amount invested at 5%: $70,000 Amount invested at 11%:$ 189,000

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.