Last week the Hannus Corporation took out three loans totalling $50,000 to fund the purchase of new equipment. Some of the money was at 6%, $1,000 more than 1/2 the amout of the 6% loan was at 8%, and the rest was at 7%. The total interest on the loans was $3,410.
Let x represent the amount borrowed at 6%, y represent the amount borrowed at 7% and z represent the amount of 8%. Write a system of equations described by the problem and solve the system.