Question

A florist 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?

Answer 1

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
-------------------
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 <==