At Rosa's Rose Shop, a bouquet containing a dozen roses costs $\$20$. If the price of a bouquet is directly proportional to the number of roses it contains, how many dollars will a bouquet of 39 roses cost?
To solve this problem, I need to find the constant of proportionality that relates the price of a bouquet to the number of roses it contains. I can use the given information that a dozen roses costs $\$20$ to find this constant. If I divide the price by the number of roses, I get the cost per rose. So, the cost per rose is $\frac{20}{12} = \frac{5}{3}$ dollars. This means that the price of a bouquet is $\frac{5}{3}$ times the number of roses it contains. To find the price of a bouquet of 39 roses, I just need to multiply $\frac{5}{3}$ by 39. So, the price of a bouquet of 39 roses is $\frac{5}{3} \times 39 = 65$ dollars. 