The price of a radio is $\$14$. The sales tax is $3\frac{1}{2}\%$. We need to find the total cost including sales tax.

1. Problem Description

The price of a radio is \14$. The sales tax is$3\frac{1}{2}\%$. We need to find the total cost including sales tax.

2. Solution Steps

First, convert the mixed number $3\frac{1}{2}$ to an improper fraction:

$3\frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{6+1}{2} = \frac{7}{2}$.

Then, convert the sales tax percentage to a decimal:

$\frac{7}{2}\% = \frac{7}{2} \times \frac{1}{100} = \frac{7}{200} = 0.035$.

Next, calculate the amount of sales tax on the radio:

Sales tax amount = Price of radio $\times$ Sales tax rate

Sales tax amount = \14 \times 0.035 = \$0.49$.

Finally, calculate the total cost of the radio including sales tax:

Total cost = Price of radio + Sales tax amount

Total cost = \14 + \0.49 = \14.49$.

3. Final Answer

The total cost including sales tax is \14.49$.