Hi John,
I can show you a couple of ways to approach this problem.
First approach:
The numbers here make the arithmetic straightforward. Since 80 is 4 times 20 and the amount paid was 13.82, the insurance paid $4 \times 13.2$ and the original cost is the sum of what you paid and what the insurance paid. Even if the numbers were not so nice, suppose you paid 18% and the insurance company 82% then the insurance company would pay $\large \frac{82}{18} \normalsize \times 13.892.$
Second approach:
Suppose that the original cost was $x$ then 13.82 is 20% of $x,$ and hence $0.20 \times x = 13.2.$ Dividing both sides by 20 you get that $x = \large \frac{13.82}{0.20}.$
Solve the problem both ways to check your arithmetic.
Penny
