Question

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 1

Answer:

12 dozens roses, 6 dozens carnations

Step-by-step explanation:

Let r be every dozen roses and c every dozen carnations.

Then, the price for $r_{n}$ dozens roses will be 23r and the price for $c_{n}$ dozens carnations will be 34c.

So the price for the total of roses and carnations together will be 480:

$23r+34c=480$          (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.

$r=2c$          (2)

then we substitute (2) in (1) as follows:

$23(2c)+34c=480\\46c+34c=480\\80c=480\\c=6$

If c=6, then r=12 for (2).

Where c and r are the dozens of each flower.