A floral shop receives a $480 order for roses and carnations. The order contains twice as many roses as carnations. The prices per dozen for the roses and carnations are $23 and $34, respectively. How many, in dozens, of each type of flower are in the order?

Answer:12 dozens roses, 6 dozens carnationsStep-by-step explanation:Let r be every dozen roses and c every dozen carnations.Then, the price for [tex]r_{n}[/tex] dozens roses will be 23r and the price for [tex]c_{n}[/tex] dozens carnations will be 34c.So the price for the total of roses and carnations together will be 480:[tex]23r+34c=480[/tex]          (1)"twice as many roses as carnations" means that if we multiply the quantity of dozens carnations by 2, it will be equal the quantity of dozens roses.[tex]r=2c[/tex]          (2)then we substitute (2) in (1) as follows:[tex]23(2c)+34c=480\\46c+34c=480\\80c=480\\c=6[/tex]If c=6, then r=12 for (2).Where c and r are the dozens of each flower.