A florist is making 5 identical bridesmaid bouquets for a wedding. she has $610 to spend and wants each bouquet to have 24 flowers. roses cost $6 each, tulips costs $4 each, and Lillies cost $3 each. she wants to have twice as many roses as any other 2 flowers combined in each bouquet. how many roses, tulips, and Lillies are in each bouquet?
Answers
Step-by-step explanation:
Given:-
A florist is making 5 identical bridesmaid bouquets for a wedding. she has $610 to spend and wants each bouquet to have 24 flowers. roses cost $6 each, tulips costs $4 each, and Lillies cost $3 each. she wants to have twice as many roses as any other 2 flowers combined in each bouquet.
To find:-
How many roses, tulips, and Lillies are in each bouquet?
Solution:-
Number of identical bridesmaid bouquets for a wedding by a florist = 5
Money spent on those bouquets = $610
The cost of each bouquet
= $610/5
= $ 122
Total number of flowers in the each bouquet = 24
Types of flowers in the bouquets = Rose, Tulip, Lilly.
Let the number of Roses be R
Let the number of Tulips be T
Let the number of Lillies be L
Given that
twice as many roses as any other 2 flowers combined in each bouquet.
Roses = 2(Tulips+ Lillies)
R = 2(T+L) ------(1)
Roses + Tulips + Lillies = 24
R + T + L = 24
=> 2(T+L ) + T + L = 24
=> 2T +2T +T+L = 24
=> 3T +3L = 24
=> 3(T+L) = 24
=> T+L = 24/3
=> T+L = 8 -------(2)
From (1)
R = 2(8)
=> R = 16
Number of Roses = 16
Cost of Rose = $6
Cost of tulip = $4
Cost of Lilly = $3
Total cost of bouquet = $ 122
6R + 4T + 3L = 122 -----(3)
=> 6(16) +4T+3L = 122
=> 96+4T+3L = 122
=> 4T+3L = 122-96
=> 4T+3L = 26 -----(4)
on multiplying (2) with 3
=>3T+3L = 24-----(5)
On Subtracting (5) from (4)
4T + 3L = 26
3T + 3L = 24
(-)
___________
T + 0 = 2
___________
T = 2
From (2)
2+L = 8
=> L = 8-2
L = 6
Number of Roses = 16
Number of Tulips = 2
Number of Lillies = 6
Answer:-
Number of Roses = 16
Number of Tulips = 2
Number of Lillies = 6
Check:-
Total number of flowers in the each bouquet
= 16+2+6
= 24
And
Number of Roses = 16
=> 2(8)
=> 2(2+6)
=> 2( Tulips+Lillies)
Number of roses is twice the sum of the number of Tulips and Lillies
Total cost of each bouquet
6R + 4T + 3L
=> 6(16)+4(2)+3(6)
=> 96+8+18
=> 122
Total cost of all 5 bouquets
= 5×122
=> Rs.610
Verified the given relations
R, T, L are the flowers in each bouquet
total budget per bouqet=cost of flowers/per bouquet
610/5=R*6 + T*4 + L*3
R=2(T+L)
24=R+T+L
that are three unknowns, three equations.