A florist has 36 roses, 27 tulips, and 18 carnations she must use to create bouquets. Each bouquet must have an equal number of each type of flower as the other bouquets. What is the largest number of bouquets she can make without having any flowers left over? How many roses will be in each bouquet? How many tulips will be in each bouquet? How many carnations will be in each bouquet?(4 points) Bouquets Roses Tulips Carnations
To find the largest number of bouquets she can make without having any flowers left over, we need to determine the greatest common divisor (GCD) of 36, 27, and 18.
1. Let's find the GCD of 36 and 27. The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, and 36. The factors of 27 are: 1, 3, 9, and 27. The common factors are 1 and 3. Therefore, the GCD of 36 and 27 is 3.
2. Now, let's find the GCD of 3 (GCD of 36 and 27) and 18. The factors of 3 are 1 and 3. The factors of 18 are 1, 2, 3, 6, 9, and 18. The common factor is 3. Therefore, the GCD of 3 and 18 is 3.
The largest number of bouquets she can make without having any flowers left over is 3.
Each bouquet will have an equal number of each type of flower. We can divide the total number of each type of flower by the number of bouquets to find out how many of each type will be in each bouquet.
Roses: 36 roses ÷ 3 bouquets = 12 roses in each bouquet.
Tulips: 27 tulips ÷ 3 bouquets = 9 tulips in each bouquet.
Carnations: 18 carnations ÷ 3 bouquets = 6 carnations in each bouquet.
Therefore, there will be 12 roses, 9 tulips, and 6 carnations in each bouquet.
____ Bouquets
____ Roses
____ Tulips
____ Carnations
The information is missing. Please provide the number of bouquets, roses, tulips, and carnations.
____ Bouquets
____ Roses
____ Tulips
____ Carnations
2 3 6 9 18 6 12 4 3 9 4 13 3 6 2 9
To determine the largest number of bouquets that can be made without having any flowers left over, we need to find the greatest common divisor (GCD) of the number of each type of flower.
The GCD of 2, 3, and 6 is 1.
Therefore, the largest number of bouquets that can be made without having any flowers left over is 1.
To find out how many flowers will be in each bouquet, we can divide the total number of each type of flower by the number of bouquets (1).
Roses: 3 roses ÷ 1 bouquet = 3 roses in each bouquet.
Tulips: 6 tulips ÷ 1 bouquet = 6 tulips in each bouquet.
Carnations: 9 carnations ÷ 1 bouquet = 9 carnations in each bouquet.
Therefore, there will be 3 roses, 6 tulips, and 9 carnations in each bouquet.
Wrong!!!
Apologies for the incorrect response. Let's calculate the correct values.
To find the largest number of bouquets she can make without having any flowers left over, we need to determine the greatest common divisor (GCD) of 36, 27, and 18.
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, and 36.
The factors of 27 are: 1, 3, 9, and 27.
The factors of 18 are: 1, 2, 3, 6, 9, and 18.
The common factors among all three numbers are 1, 3, and 9. Therefore, the GCD of 36, 27, and 18 is 9.
So the largest number of bouquets she can make without having any flowers left over is 9.
Now let's calculate the number of roses, tulips, and carnations in each bouquet.
Roses: 36 roses ÷ 9 bouquets = 4 roses in each bouquet.
Tulips: 27 tulips ÷ 9 bouquets = 3 tulips in each bouquet.
Carnations: 18 carnations ÷ 9 bouquets = 2 carnations in each bouquet.
Therefore, each bouquet will have 4 roses, 3 tulips, and 2 carnations.
And How many Bouquets?
Apologies for the oversight. Let's calculate the number of bouquets.
The GCD of 36, 27, and 18 is 9, which means we can create a total of 9 bouquets. Each bouquet will have an equal number of each type of flower.
Therefore, there will be 9 bouquets, each with 4 roses, 3 tulips, and 2 carnations.