A florist has 36 roses, 27 tulips, and 18 carnations she must use to create bouquets. each bouquets 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?
_ bouquets
_ roses in each bouquet
_tulips in each bouquet
_carnations in each bouquet
To find the largest number of bouquets she can make without having any flowers left over, we need to find the greatest common divisor (GCD) of the numbers of each type of flower.
The GCD of 36, 27, and 18 is 9.
Therefore, the florist can make 9 bouquets.
In each bouquet, there will be:
- 36 roses / 9 bouquets = 4 roses in each bouquet
- 27 tulips / 9 bouquets = 3 tulips in each bouquet
- 18 carnations / 9 bouquets = 2 carnations in each bouquet.
To determine the largest number of bouquets the florist can make without any flowers left over, let's find the greatest common divisor (GCD) of 36, 27, and 18. The GCD will represent the maximum number of bouquets.
The GCD of 36, 27, and 18 is 9.
Therefore, the florist can make 9 bouquets.
To find the number of roses, tulips, and carnations in each bouquet, we divide the total number of flowers by the number of bouquets.
Number of roses in each bouquet = 36 roses / 9 bouquets = 4 roses
Number of tulips in each bouquet = 27 tulips / 9 bouquets = 3 tulips
Number of carnations in each bouquet = 18 carnations / 9 bouquets = 2 carnations
So, the florist can create 9 bouquets, with each bouquet containing 4 roses, 3 tulips, and 2 carnations.
To find the number of bouquets the florist can make without any flowers left over, we need to find the greatest common divisor (GCD) of the number of roses, tulips, and carnations she has. The GCD represents the largest equal parts we can divide each quantity by.
First, we can find the GCD of 36, 27, and 18. One way to do this is to list the factors of each number:
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 27: 1, 3, 9, 27
Factors of 18: 1, 2, 3, 6, 9, 18
From the common factors, we can see that the GCD is 9.
Therefore, the florist can make the largest number of bouquets without any flowers left over by dividing each quantity by 9:
Number of bouquets: 9 bouquets (since the GCD is 9)
Number of roses in each bouquet: 36 roses ÷ 9 bouquets = 4 roses in each bouquet
Number of tulips in each bouquet: 27 tulips ÷ 9 bouquets = 3 tulips in each bouquet
Number of carnations in each bouquet: 18 carnations ÷ 9 bouquets = 2 carnations in each bouquet
So, the answers are:
Number of bouquets: 9 bouquets
Number of roses in each bouquet: 4 roses
Number of tulips in each bouquet: 3 tulips
Number of carnations in each bouquet: 2 carnations