Translate to a system of equations and solve:

Jill’s Sandwich Shoppe owes \(65,200 on two business loans, one at 4.5% interest and the other at 7.2% interest. The total amount of interest owed last year was \)3,582. What was the principal for each loan?

The given data is that Jill’s Sandwich Shoppe owes $65,200 on two business loans, one at 4.5% interest and the other at 7.2% interest. The total amount of interest owed last year was $3,582.

Let x be the principal amount on first loan and ybe the principal amount on second loan.

Total loan owes is $65200 that is $x+y=65200--\left(1\right)$

The total amount of interest she paid is $3582.

As we are given the interest rates of both the loans thus, the expression is equal to$0.045x+0.072y=3582--\left(2\right)$

Multiply equation (1) with $0.072$and write the revised equation.

$$\begin{gathered} 0.072(x+y)=0.072\left(65200\right) \\ 0.072x+0.072y=4694.4--\left(3\right) \end{gathered}$$

Solve the equations (2) and (3) by subtracting equation (2) from equation (3) to find the value ofx.

$$\begin{gathered} 0.072x+0.072y-0.045x-0.072y=4694.4-3582 \\ 0.027x=1112.4 \\ x=41200 \end{gathered}$$