Expert: Josh - 10/23/2006

Question
you borrow a total of $3000 for school. Part of the money you borrowed is from a credit union that charges 8% simple interest, and the rest of it is from a bank that charges 10% simple interest. At the end of one year, your total interest owed is $277.50. how much of the original $3000 came from the credit union?

Answer
There are two unknowns in this question. The amount borrowed from a credit union (at 8% interest) and amount borrowed from the bank (at 10% interest). Let's denote these by "x" and "y" respectively. They must add up to $3000, so we have x+y=3000....[#1]

The total interest charged must be given by 277.5=x*0.08+y*0.10....[#2]

To eliminate one unknown, we can substitute y=3000-x (from [#1]) into expression [#2].

This gives 277.5=0.08x+0.1(3000-x), which simplifies to 277.5=0.08x-0.1x+300 and reduces to 0.02x=(300-277.5).
Therefore, the amount borrowed from the credit union is x=(300-277.5)/0.02=1125.

It follows from [#1] that the amount borrowed from the bank, y=3000-(300-277.5)/0.02=1875.