Our simple interest formula is I = prt, where I is the amount of interest, p is the amount of principal, r is the percentage written as a decimal, and t is the amount of time (in this case in years). We will define our variable x as the amount borrowed at the lower percentage rate. Our formula would then look like
. (Remember that when we convert percentages to decimals, we divide by 100; 3.5/100 = 0.035.)
The remaining money borrowed was invested at 7% interest. The expression to represent the remaining money would be 6000 - x, as it is what was left over to borrow. The interest formula for this loan would be
. (Again, we must divide 7 by 100 to convert the percentage; 7/100=0.07.)
Using the distributive property we have:
(t in this case is 1, since it is 1 year.)
The total amount of interest for both loans for one year was $259, so we have:
Combine our like terms:
Cancel 420 by subtracting:
Cancel -0.035 by dividing:
This means she borrowed $4600 at the lower interest rate. The remainder would be $6000-$4600=$1400 at the higher interest rate.
