Problema Solution
A broker made two separate investments on behalf of a client. The first investment earned 12% and the second investment lost 5%, for a total gain of $1040. If the amounts in these two investments had been switched, then the result would have been a gain of $360. Determine how much was actually invested at each rate.
Answer provided by our tutors
First investment is A and the second investment B
Then 0.12A - 0.05B = 1040 =>12A-4B=104000----1
and 0.12B - 0.05A = 360 => 12B - 5A = 36000.....(2)
(1) x 5 => 60A - 25B = 520000
(2) x 12 => 144B - 60A = 432000
adding gives: 119B = 952000 => B = 8000, so A = 12000
So, $12000 and $8000 are invested at 12% and 5% respectively.