A technician is starting a new repair shop and takes out two loans to purchase necessary equipment. The first loan has an interest rate of 5%, and the second loan has an interest rate of 8%. The total amount borrowed is 15,000 dollars, and the total annual interest paid is 900 dollars. Let $x$ represent the principal amount of the 5% loan and $y$ represent the principal amount of the 8% loan. Match each mathematical component to its correct financial description in the system of equations.

A bakery owner takes out two loans totaling $15,000 to purchase new commercial ovens. The first loan has an annual interest rate of ${}5\%$, and the second loan has an annual interest rate of ${}7\%$. If the total interest paid after one year is $900, which equation correctly represents the total interest paid on these two loans? (Let $x$ be the principal of the ${}5\%$ loan and $y$ be the principal of the ${}7\%$ loan).

Financing Business Equipment

A logistics coordinator is analyzing two different equipment loans using a system of equations to determine the amount borrowed for each. While the sum of the two loan amounts is used to create the principal equation, the annual interest rates (such as {}5.5% and {}7.25%) must be used as coefficients in the ____ equation.

A small business owner is using a system of equations to determine the original principal amounts of two separate loans used to buy office equipment.

True or False: To build the interest equation for this system, the owner should multiply the total combined principal by the sum of the two interest rates.

A small business consultant is writing a guide to help new entrepreneurs determine how their total startup debt is split between two distinct loans. Arrange the standard mathematical steps for setting up and solving this loan interest application in the correct logical order.

Setting Up Loan Interest Systems