A realtor borrowed 80000 to develop some property He was abl

A realtor borrowed $80,000 to develop some property. He was able to borrow part of the money at 4.5% interest and the rest at 5%. The annual interest on the two loan amounts was $7,600. How much was borrowed at each rate?

~~~Please show work

Solution

Let $ x was borrowed at 4.5% rate and hence $(80000- x) was borrowed at rate of 5%.

THen annual interest on loan for the first part is $ [ x*(4.5/100)*1(year) ]...........(1)

And interest on the second part is similarly $ [(80000-x)*(5/100)*1 (year) ].............(2)

Accumulating these two interests we have ,

4.5x/100 + (80000-x)*5/100 = 760

=> 80000/100 + (4.5-5)*x/100 = 760

=>(80000-760000) = 0.5x

=>x/2= -680000

=> x = -1360000.

Now x cannot be negative . So the figures for total interest amount is wrong.

Also we can see that if the entire amount $80000 was borrowed at rate 5% per year then the total interest would have been $80000*5/100 = $4000 < $7600 .

So the data given is wrong.