I need help on this math problem

Question

Chelsea took out three loans for a total of ?$79,000 to start an organic orchard. Her? business-equipment loan was at an interest rate of? 11%, the? small-business loan was at an interest rate of 4?%, and her? home-equity loan was at an interest rate of 5.5?%. The total simple interest due on the loans in one year was ?$4795. The annual simple interest on the? home-equity loan was ?$495 more than the interest on the? business-equipment loan. How much did she borrow from each? source?

 

sources being the business-equipment loan, small business loan, and home equity loan.

 

 

Answer 1

1. X + Y + Z = $79,000 {Eqn 1}where X is her business equipment loan amount, Y the small business loan amount, and Z the home equity loan amount.
2. To figure out the interest paid in one year, multiply the rate of the loan by loan amount.  For example, if you took out a 10% loan on $1000, you would owe 0.10 * $1000 = $100 in interest payment at the end of the year.
3. 0.11X + 0.04Y + .055Z = $4795  (Eqn 2}
4. 0.04Y represents the interest on the small business loan.  Similarly, 0.11X is the interest on the business equipment loan.  So, we have 0.055Z = 0.11X + $495  {Eqn 3}
5. Three equations, three unknowns.  You can now solve the problem in a number of ways.  I would start by finding an equation for Z in Eqn 3.  Once you have Z, substituted it into Eqns 1 and 2.  You will now have two equations and two unknowns (X & Y).  Do you know how to solve it from that point?  If not, let me know.