a florist is making 5 identical bridesmaid bouquets for wedding. she has $510 to spend and wants 20 flowers for each bouquet. roses cost $4 each,tulips cost$2 each and lilies cost $3 each. she wants to have twice as many roses as the other 2 flowers combined in each bouquet. find total number of flowers are there
For each bouquet:
Number of lilies --- x
number of tulips --- y
number of roses --- 2x + 2y , where both x and y are whole numbers
then x+y + 2x+2y = 20
3x + 3y = 20
x + y = 20/3 <----- trouble ahead: how can the sum of 2 whole numbers be a fraction?
cost per bouquet = 510/5 = 102
so 3x + 2y + 4(2x+2y) = 102
11x + 10y = 102
first one times 10
10x + 10y = 200/3
11x + 10y = 102
subtract:
x = 106/3
y = -86/3 <----- good one!
2x + 2y = -172/3
check: 3x + 3y = 3(106/3 + (-86/3) = 20
total cost: 5(3x + 2y + 4(2x+2y))
= 55x + 50y
= 55(106/3) + 50(-86/3) = 510
So my "solution" to your problem makes mathematical sense,
but not in the real world.
I could have stopped at x + y = 20/3
but I continued to show you the steps you can follow after you fix the problem.
pinga
pinga
To find the total number of flowers needed, we need to determine the number of roses, tulips, and lilies in each bouquet and then calculate the total for all five bouquets.
Let's start by determining the number of roses, tulips, and lilies in each bouquet.
Since the florist wants twice as many roses as the other two flowers combined, let's say the number of roses is "x".
Then, the combined number of tulips and lilies would be (x/2), as the number of roses is twice that of the other two flowers combined.
In each bouquet, we have:
Roses: x
Tulips: (x/2)
Lilies: (x/2)
Since the florist wants 20 flowers in each bouquet, we can write the equation:
x + (x/2) + (x/2) = 20
Now, let's solve the equation to find the value of 'x':
x + x/2 + x/2 = 20
(2x + x + x)/2 = 20
(4x)/2 = 20
4x = 40
x = 40/4
x = 10
So, in each bouquet, there are 10 roses, 5 tulips, and 5 lilies.
Now, let's calculate the total cost of all the flowers.
The price per rose is $4, so 10 roses will cost: 10 x $4 = $40.
The price per tulip is $2, so 5 tulips will cost: 5 x $2 = $10.
The price per lily is $3, so 5 lilies will cost: 5 x $3 = $15.
In each bouquet, the total cost of flowers is: $40 + $10 + $15 = $65.
Since there are five bouquets, the total cost of all the flowers is: $65 x 5 = $325.
Therefore, there are a total of 325 flowers for all five bouquets.