Aflorist is making 5 identical bridesmaid bouquets for a wedding. she has $610 to spend (including tax) and wants 24 flowers for each bouquet. roses cost $6 each, tulips cost $4 each, and lilies cost $3 each. she wants to have twice as many roses as the other 2 flowers combined in each bouquet. how many roses, tulips, and lilies are in each bouquet?

Each bouquet has 16 roses, 6 lilies and 2 tulips.

Since a florist is making 5 identical bridesmaid bouquets for a wedding, and she has $ 610 to spend (including tax) and wants 24 flowers for each bouquet, roses cost $ 6 each, tulips cost $ 4 each, and lilies cost $ 3 each, and she wants to have twice as many roses as the other 2 flowers combined in each bouquet, to determine how many roses, tulips, and lilies are in each bouquet, the following calculation must be performed:

-First, 24 must be divided into three equal parts, and two of those three parts must be assigned to the roses. Then, the different alternatives of floral combinations must be calculated until the desired value is reached.

(24/3) x 2 = X 8 x 2 = X 16 = X Therefore, there are 16 roses in each bouquet. (16 x 6 + 7 x 4 + 1 x 3) x 5 = (96 + 28 + 3) x 5 = 635 (16 x 6 + 1 x 4 + 7 x 3) x 5 = (96 + 4 + 21) x 5 = 605 (16 x 6 + 2 x 4 + 6 x 3) x 5 = (96 + 8 + 18) x 5 = 610

Therefore, each bouquet has 16 roses, 6 lilies and 2 tulips.

R + t + L = 5(24).....r + t + L = 120
6r + 4t + 3L = 610
r = 2(t + L).......r = 2t + 2L

2t + 2L + t + L = 120
3t + 3L = 120

6(2t + 2L) + 4t + 3L = 610
12t + 12L + 4t + 3L = 610
16t + 15L = 610

16t + 15L = 610
3t + 3L = 120 ...multiply by -5
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16t + 15L = 610
-15t - 15L = - 600 (result of multiplying by -5)
-------------------add
t = 10

3t + 3L = 120
3(10) + 3L = 120
30 + 3L = 120
3L = 120 - 30
3L = 90
L = 90/3
L = 30

r = 2(t + L)
r = 2(10 + 30)
r = 2(40)
r = 80

so for all the bouquets, there are 80 roses, 30 lillies, and 10 tulips....but there are 5 bouquets...

so each bouquet has : 
80/5 = 16 roses <==
10/5 = 2 tulips <==
30/5 = 6 lillies <==

35.

2*2= 4*2=8

3*3=9*3=27

27+8=35

So the answer is 35. Hope this helps