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?

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Answer 1 · 2017-12-20T06:27:13

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

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

There is a given relationship between the two amounts, so you can define them using one 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#

'Interest at #5%# + Interest at #11% = 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#