Question

A merchant has two loans totaling $25,000. The simple interest rates are 7% and 8%. If the annual interest charge on the 7% loan is $250 more than on the 8% loan, how much did he borrow at each rate?

Answer 1

Alright, since 7% is 0.07 (put 2 decimal places in front of the percentage to get the decimal), we know that 0.07*the loan amount of the 7% loan=0.08*the loan amount of the 8% loan+250. If the 7% loan is x and the 0.08 loan is y, we have 0.07*x=0.08*y+250. We also know that x+y=25000, so if we subtract y from both sides of the equation we have 25000-y=x. Plugging that into 0.07*x=0.08*y+250, we get 0.07*(25000-y)=0.08*y+250
=1750-0.07y=0.08y+250. Multiplying both sides by 100 (to get integers), we get 175000-7y=8y+25000. Adding 7y to both sides, as well as subtracting 25000 from both sides, we get 150000=15y and by dividing by 15 we get
y=10000= the 8% loan amount. Since 25000-y=x,
25000-10000=15000=the 7% loan amount