Answer
$\$ 9.96$
Work Step by Step
Let us consider that:
$\text{x=cost of a package of bacon, and}$ $\text{y =cost of a carton of eggs}$
We are given that the two system of equations as follows:
$3x+2y=13.45~~~~(1) $
and
$2x+3y=11.45~~~~(2)$
We multiply equation (1) by $3$ and equation (2) by $-2$ and obtain:
$9x+6y=40.35~~~~(3)$ and $−4x−6y=−22.90 ~~~~(4)$
We add equations (3) and (4) to obtain:
$5x=17.45 \implies x=3.49$
Now, back-substitute the value of $x$ into Equation (3) to solve for $y$:
$(9)(3.49)+6y=40.35 \implies y=1.49$
Therefore, the price we want to refund will be:
$2×3.49+2×1.49=6.98+2.98=\$ 9.96$
