A business orders 215 flowers for their employees on Valentine's Day. Roses cost $3.00 each, carnations cost $1.00 each, and lilies cost $2.00 each. There are 15 more lilies than roses. The total of the order came to $410.00. How many of each type of flower were ordered?

Let, number of roses, carnations and lilies are x, y and z respectively.

So,

x + y + z = 215    1 )

It is given that total cost is $410.00 :

3x + y + 2z = 410    2 )

Also, there are 15 more lilies than roses.

z = x + 15    3 )

Putting value of z in eq 1 and 2 , we get :

x + y + x + 15 = 215

2x + y = 200     4 )

3x + y + 2( x + 15 ) = 410

5x + y = 380     5 )

Solving equation 4 and 5, we get :

3x = 180

x = 60

z = 60 + 15 = 75

y = 215 - 60 - 75 = 80

Therefore, number of roses, carnations and lilies are 60, 80 and 75 respectively.

Hence, this is the required solution.