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

12 dozens roses, 6 dozens carnations

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.