Our simple interest formula is <em>I = prt</em>, where <em>I</em> is the amount of interest, <em>p</em> is the amount of principal, <em>r</em> is the percentage written as a decimal, and <em>t</em> is the amount of time (in this case in years). We will define our variable <em>x</em> 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 - <em>x</em>, 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:
(<em>t</em> 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.